Download Angles, Triangles, and Quadrilaterals

Enhanced Instructional Transition Guide
Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Unit 06 Geometry: Angles, Triangles, and Quadrilaterals (10 days)
Possible Lesson 01 (10 days)
POSSIBLE LESSON 01 (10 days)
This lesson is one approach to teaching the State Standards associated with this unit. Districts are encouraged to customize this lesson by supplementing
with district-approved resources, materials, and activities to best meet the needs of learners. The duration for this lesson is only a recommendation, and
districts may modify the time frame to meet students’ needs. To better understand how your district is implementing CSCOPE lessons, please contact your
child’s teacher. (For your convenience, please find linked the TEA Commissioner’s List of State Board of Education Approved Instructional Resources and
Midcycle State Adopted Instructional Materials.)
Lesson Synopsis:
Students classify angles by estimating angle measures and using a protractor to find exact angle measures. Students construct angles with a protractor and expand their
understanding of classifying angles by exploring angle relationships in triangles and quadrilaterals.
TEKS:
The Texas Essential Knowledge and Skills (TEKS) listed below are the standards adopted by the State Board of Education, which are required by Texas
law. Any standard that has a strike-through (e.g. sample phrase) indicates that portion of the standard is taught in a previous or subsequent unit.
The TEKS are available on the Texas Education Agency website at http://www.tea.state.tx.us/index2.aspx?id=6148
6.6
Geometry and spatial reasoning.. The student uses geometric vocabulary to describe angles, polygons, and circles. The student is
expected to:
6.6A
Use angle measurements to classify angles as acute, obtuse, or right.
Supporting Standard
6.6B
Identify relationships involving angles in triangles and quadrilaterals.
Supporting Standard
6.8
Measurement.. The student solves application problems involving estimation and measurement of length, area, time, temperature,
volume, weight, and angles. The student is expected to:
6.8C
Measure angles.
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Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Supporting Standard
Underlying Processes and Mathematical Tools TEKS:
6.11
Underlying processes and mathematical tools.. The student applies Grade 6 mathematics to solve problems connected to everyday
experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:
6.11B
Use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating
the solution for reasonableness.
6.11C
Select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking
for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards
to solve a problem.
6.11D
Select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation,
and number sense to solve problems.
6.13
Underlying processes and mathematical tools.. The student uses logical reasoning to make conjectures and verify conclusions. The
student is expected to:
6.13A
Make conjectures from patterns or sets of examples and nonexamples.
6.13B
Validate his/her conclusions using mathematical properties and relationships.
Performance Indicator(s):
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Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Grade6 Mathematics Unit06 PI01
Use a drawing of a triangle or quadrilateral to find each angle measurement and classification. Generate a model (e.g., sketch, computer-generated, etc.) of the drawing, and
label the angle measure using measurement notation and the classification (e.g., acute, obtuse, or right) for each angle. Validate each measure by explaining the angle
relationships and problem-solving processes.
Sample Performance Indicator:
A government surveyor provided the following diagram of the new city park land. Sketch the diagram, and label the angle measure using
measurement notation and the classification for each angle. Justify each measure by explaining the angle relationships and problem-solving
processes.
Standard(s): 6.6A , 6.6B , 6.8C , 6.11B , 6.11C , 6.11D , 6.13A , 6.13B
ELPS ELPS.c.1C , ELPS.c.3H
Key Understanding(s):
Estimation of an angle measure prior to directly measuring the angle will help prevent misreading the scale on the protractor.
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Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Protractors are tools used to measure angles using degrees.
Angle classifications can be validated by their measure.
Triangle classifications can be validated by the measure of their angles.
Relationships between the angles in triangles and quadrilaterals can be validated, as the sum of the angles of all triangles is 180° while the sum of the angles of all
quadrilaterals is 360°.
Conjectures about a missing angle measure of a triangle can be validated and solved if two other angle measures are known.
Conjectures about a missing angle measure of a quadrilateral can be validated and solved if three other angle measures are known.
When determining missing angle measures in a problem situation involving a triangle or quadrilateral, a problem-solving process can be used to examine the
known angles, make and carry out a plan to find the missing angles, and evaluate the angle measures for reasonableness.
Misconception(s):
Some students may think that degree measure for angles is read from only one side of a protractor. For example: An angle with a measure of 30° may be at the
markings of 30° and 150° on the protractor.
Some students may think that when measuring with a protractor, one of the two rays must always align with zero. The accurate measure is dependent upon the
difference in the beginning and ending measure. For example, an angle with a measure of 30° can be determined by beginning at 0° and ending at 30° or by finding
the difference between other ending and starting points, such as 180° ­ 150°, 100° ­ 70°, etc.
Some students may misalign the vertex and ray of an angle on the protractor.
Vocabulary of Instruction:
acute
angle
congruent
degrees
equiangular
equilateral
isosceles triangle
obtuse
polygon
protractor
quadrilateral
ray
regular polygon
right
right angle
scalene triangle
straight
triangle
vertex
page 4 of 93 Enhanced Instructional Transition Guide
Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Materials List:
cardstock (1 sheet per 2 students)
cardstock (1 sheet per 4 students)
cardstock (7 sheets per teacher)
display protractor (1 per teacher)
markers (1 set per teacher)
paper (plain) (1 sheet per student)
paper (plain) (1 sheet per student, 1 sheet per teacher)
patty paper (1 per student)
patty paper (3 sheets per student)
plastic zip bag (sandwich sized) (1 per 2 students)
plastic zip bag (sandwich sized) (1 per 4 students)
plastic zip bag (sandwich sized) (1 per teacher)
protractor (1 per student, 1 per teacher)
ruler (1 per student, 1 per teacher)
scissors (1 per student)
scissors (1 per teacher)
Attachments:
All attachments associated with this lesson are referenced in the body of the lesson. Due to considerations for grading or student assessment, attachments
that are connected with Performance Indicators or serve as answer keys are available in the district site and are not accessible on the public website.
What's My Angle? KEY
What’s My Angle?
What’s My Angle Measure? KEY
What’s My Angle Measure?
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Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Measuring with a Protractor KEY
Measuring with a Protractor
How Many Degrees? KEY
How Many Degrees?
Naming Angles KEY
Naming Angles
Notes – Drawing an Angle with a Protractor
Artistic Angles
Classifying Triangles
Triangle Template Directions KEY
Triangle Template Directions
Angle Relationships in Triangles KEY
Angle Relationships in Triangles
Missing Angle Measures in Triangles KEY
Missing Angle Measures in Triangles
Angle Relationships in Quadrilaterals KEY
Angle Relationships in Quadrilaterals
Missing Angle Measures in Quadrilaterals KEY
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Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Missing Angle Measures in Quadrilaterals
Sum of Angles KEY
Sum of Angles
I Have, Who Has?
Polygon Angle Evaluation KEY
Polygon Angle Evaluation
GETTING READY FOR INSTRUCTION
Teachers are encouraged to supplement and substitute resources, materials, and activities to meet the needs of learners. These lessons are one approach to
teaching the TEKS/Specificity as well as addressing the Performance Indicators associated with each unit. District personnel may create original lessons using
the Content Creator in the Tools Tab. All originally authored lessons can be saved in the “My CSCOPE” Tab within the “My Content” area. Suggested
Day
1
Suggested Instructional Procedures
Notes for Teacher
Topics:
Spiraling Review
Angles
Engage 1
Students use logic and reasoning skills to sort a group of angles by their attributes.
ATTACHMENTS
Card Set: What’s My Angle? (1 per 4 students)
Instructional Procedures:
MATERIALS
1. Prior to instruction, create a card set: What’s My Angle? for every 4 students by copying on
cardstock, cutting apart, and placing in a plastic zip bag.
cardstock (1 sheet per 4 students)
page 7 of 93 Enhanced Instructional Transition Guide
Suggested
Day
Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Suggested Instructional Procedures
2. Place students in groups of 4 and distribute card set: What’s My Angle? to each group.
Instruct student groups to sort the angles into groups according to their attributes. Allow time
for students to complete the activity. Monitor and assess student groups to check for
Notes for Teacher
scissors (1 per teacher)
plastic zip bag (sandwich sized) (1 per 4
students)
understanding. Facilitate a class discussion about the attributes used to create the grouping
of angles.
Topics:
ATTACHMENTS
Angle measurement
Teacher Resource: What’s My Angle
Angle classification
Measure? KEY (1 per teacher)
Teacher Resource: What’s My Angle
Explore/Explain 1
Measure? (1 per teacher)
Students formalize the definitions of an acute, obtuse, right, and straight angle. Students explore
Handout: What’s My Angle Measure? (1 per
measuring and classifying angles using a protractor.
student)
Instructional Procedures:
MATERIALS
1. Place students in groups of 4. Distribute a protractor to each student. Instruct students to
examine the protractor and discuss with their group how they think you should use a
protractor (1 per student)
protractor. Allow 1 – 2 minutes for students to complete their examinations and discussions.
display protractor (1 per teacher)
Monitor and assess student groups to check for understanding.
2. Display a protractor for the class to see. Facilitate a class discussion about how to use a
protractor. Demonstrate how to measure several types of angles using a protractor.
3. Display teacher resource: What’s My Angle Measure?.
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Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Suggested Instructional Procedures
Notes for Teacher
4. Distribute handout: What’s My Angle Measure? to each student. Instruct student groups to
measure and classify each angle. Allow time for students to complete the activity. Monitor
and assess student groups to check for understanding. Facilitate a class discussion about
classifying angles and measuring angles with a protractor.
Ask:
What is the vertex of the angle? (The point where the two rays meet.)
How do you place the protractor to measure an angle? (Center the vertex of the
angle in the center mark of the protractor, and align one of the rays along the 0° mark.)
How do you know how many degrees the angle measures? (Read the degree
marking on the protractor for the other ray. Read the correct marking so the measure for
the angle is reasonable.)
Why are there two rows of numbers on the protractor? (Because the angle can open
up in either direction.)
How do you know which numbers to use? (Use the number that is in the same row of
numbers as the zero that the other ray is lined up with.)
How do you classify the angle? Answers may vary. Acute angles measure between 0
and 90 degrees; right angles measure exactly 90 degrees; obtuse angles measure
between 90 and 180 degrees; straight angles measure exactly 180 degrees; etc.
2
Topics:
Spiraling Review
Angle measurement
Angle classification
Explore/Explain 2
ATTACHMENTS
Teacher Resource: How Many Degrees? KEY
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Unit 06:
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Suggested Instructional Procedures
Notes for Teacher
Students use a protractor to measure and classify angles. Students explore measuring angles
(1 per teacher)
with a protractor.
Handout: How Many Degrees? (1 per student)
Instructional Procedures:
MATERIALS
1. Place students in pairs. Distribute handout: How Many Degrees? and a protractor to each
student. Instruct student pairs to classify each angle, estimate the measure of each angle
protractor (1 per student)
measure, measure each angle using a protractor, and then check the measurement for
reasonableness. Allow time for student pairs to complete the activity. Monitor and assess
student pairs to check for understanding. Facilitate a class discussion about measuring
angles.
Ask:
How are protractors used to measure angles in degrees? (Center the vertex of the
angle in the center mark of the protractor, align one of the rays along the 0° mark, and
read the degree marking on the protractor for the other ray. Read the correct marking so
the measure for the angle is reasonable.)
What are you measuring when you measure angles? (the turn of the ray, the
measure of rotation of a ray in degrees)
What strategy will you use to measure the angles? Answers may vary. Some
possible answers include placing the center of the straight angle on the protractor at the
vertex of the angle and aligning one of the rays at 0°.
What can you do if the ray is not long enough to reach the numbers on the
protractor? Answers may vary. You extend the ray of the angle; you can use a piece of
paper to extend the length of the ray; you can use a straight edge to extend the length of
the ray.
page 10 of 93 Enhanced Instructional Transition Guide
Suggested
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Suggested Instructional Procedures
Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Notes for Teacher
Model extending the rays of an angle and measuring the angle, if necessary
How did you measure the angles that appeared to be turned in different
directions? (by turning the protractor or the paper) (Model turning the paper or protractor
to measure an angle, if necessary)
2. Facilitate a class discussion to debrief student solutions about the strategies used to
classify, estimate, measure, and check each angle measurement for reasonableness on
their handout: How Many Degrees?.
Ask:
Did the angle you were measuring appear to be less than, equal to, or greater
than 90°? Answers may vary. If the angle is closed more than 90°, the measure of the
angle is less than 90°; etc.
How can classifications of angles help you in estimating angle measures?
(Classifying angles, prior to estimating and measuring, helps you have a range of
numbers in mind that would be reasonable for the measure of the angle and would keep
you from misreading the protractor.)
How did you estimate the angle measures in the handout: How Many Degrees? (I
compared the angle measure to a 90° angle to determine the angle classification.)
What can you do if the rays of the angle are not long enough to reach the lines
on the protractor? (Draw a line to extend the rays.)
How did you measure the angles that appeared to be turned in different
directions? (by turning the protractor or the paper)
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Day
Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Suggested Instructional Procedures
Topics:
Notes for Teacher
ATTACHMENTS
Angle measurement
Teacher Resource: Measuring with a
Angle classification
Protractor KEY (1 per teacher)
Handout: Measuring with a Protractor (1 per
Elaborate 1
student)
Students apply their knowledge of measuring and classifying angles using a protractor to
measure and classify angles using a pictorial model of a protractor.
Instructional Procedures:
1. Place students in pairs. Distribute handout: Measuring with a Protractor. Instruct student
pairs to complete problems 1 and 2. Allow time for students to complete the activity. Monitor
and assess student pairs to check for understanding. Facilitate a class discussion to debrief
student solutions.
Ask:
What is the angle measure for problem 1? (130°)
How did you get 130° for problem 1? Answers may vary. Since one of the rays lined
up with zero, I used the number the other ray was lined up with, using the same row of
numbers; I subtracted 50° from 180° to get 130°; I subtracted 0° from 130° to get 130°;
etc.
What is the angle classification for Problem 1? (obtuse) Why? (The angle measures
between 90 and 180 degrees.)
What is the angle measure for problem 2? (100°)
How did you get 100° for problem 2? (Since neither ray lined up with a zero, I had to
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Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Notes for Teacher
subtract the two numbers that were in the same row for each ray of the angle.)
What is the angle classification for Problem 2? (obtuse) Why? (The angle measures
between 90 and 180 degrees.)
How can I use the angle classification to determine reasonableness? (I can use
the definition of the angle classification to determine if the angle measure agrees with the
classification.)
2. Instruct student pairs to complete the remainder of handout: Measuring with a Protractor.
Allow time for students to complete the activity. Monitor and assess student pairs to check
for understanding. Facilitate a class discussion to debrief student solutions.
Ask:
How can classifications of angles help us in calculating angle measures?
(Classifying angles, prior to calculating the measure, of the angle helps us have a range
of numbers in mind that would be reasonable for the measure of the angle and would
keep us from misreading the protractor.)
How can you determine the classification of an angle? (angles less than 90° but
greater than 0° are acute angles; right angles are exactly 90°; angles that are greater than
90° but less than 180° are obtuse angles; and straight angles are exactly 180°)
How can you calculate the measure of an angle if neither ray is lined up with
zero? (Subtract the numbers that are in the same row for each ray of the angle.)
Does it matter which set of numbers are used to calculate the measure of the
angle? (No, as long as the numbers that are used are in the same row of numbers.)
page 13 of 93 Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Enhanced Instructional Transition Guide
Suggested
Day
3
Suggested Instructional Procedures
Notes for Teacher
Topics:
Spiraling Review
Angle measurement
ATTACHMENTS
Explore/Explain 3
Students use the angle symbol with letters or numbers to name angles.
Teacher Resource: Naming Angles KEY (1 per
teacher)
Instructional Procedures:
Teacher Resource: Naming Angles (1 per
teacher)
1. Place students in groups of 4. Display teacher resource: Naming Angles.
Ask:
What if I told you to measure “Angle A” in Figure 1? Would you be able to
measure the angle? (No, there is more than one “angle A.”)
MATERIALS
markers (1 set per teacher)
How could you determine which “Angle A” I wanted you to measure? (Ask which
rays are part of the angle.)
What if I asked you to measure “Angle BAC”? Would you be able to measure the
TEACHER NOTE
angle? (Yes, I can identify the angle.)
The teacher may want to use different color markers to
Why do you think it is important for us to name angles? (to specifically identify the
draw in arcs for each angle in Figure 1 when writing the
angle to be measured or discussed)
degree measure of each angle. Refer to Figure 1 from
the KEY for handout: Naming Angles.
2. Record the following for the class to see:
BAC.
Ask:
Does the order of the letters matter in the name of angles? (Yes, the vertex must
be in the center.)
Name the angles that appear to be a right angle. ( CAE,
EAC,
BAD,
DAB,
page 14 of 93 Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Enhanced Instructional Transition Guide
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DAF,
Notes for Teacher
FAD) How do you know? (They appear to be 90°.)
Name the angles that appear to be obtuse. ( CAF,
FAC,
BAE,
EAB) How do
you know? (They are greater than 90°.)
Name the angles that appear to be acute. ( BAC,
EAD,
EAF,
CAB,
CAD,
DAC,
DAE,
FAE) How do you know? (They are less than 90°.)
Which of these angles are about 135°? ( CAF,
FAC,
BAE,
EAB) Would you
have to measure or could you just look at each angle to estimate? (You can look
to see how they compare to 90°.)
How many right angles can be in a straight angle? (2) How do you know? (90° +
90° = 180°)
How many obtuse angles can be in a straight angle? (1) How do you know? (An
obtuse angle is greater than 90° but less than 180°, so there can only be one obtuse
angle in a straight angle.)
If there is a straight angle that is made of one obtuse angle and another angle,
what is the classification of the other angle? (an acute angle) How do you know?
(Since a straight angle is 180°, and an obtuse angle is greater than 90° but less than
180°, then the smallest measure the obtuse angle can be is 91°, because 180° - 91° =
89°, and 89° is an acute angle.)
How many obtuse angles can be in a right angle? (0) How do you know? (An
obtuse angle has a greater measure than a right angle.)
Can there be more than one acute angle in a right angle? (yes) How do you
know? (Acute angles are less than 90°; therefore if a right angle is made up of two
angles, they both have to be acute.)
What if I told you to measure “Angle A” in figure 2? Would you be able to
measure the angle? (Yes, there is only one “angle A.”)
page 15 of 93 Enhanced Instructional Transition Guide
Suggested
Day
Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Suggested Instructional Procedures
Notes for Teacher
Name two acute angle measures that make up a right angle. Answers may vary. A
30° and a 60°; a 45° and a 45°; a 70° and a 20°; etc. How do you know? (They have to
add up to 90° to make a right angle.)
What is different about figure 3? (It uses numbers instead of letters.)
3. Using the displayed teacher resource: Naming Angles, facilitate a class discussion about
how to name all angles in the problem, including using the degree symbol, the angle symbol,
and the “m ” to indicate the degree measure of an angle.
Topics:
ATTACHMENTS
Angle construction
Teacher Resource: Notes – Drawing an Angle
Angle measurement
with a Protractor (1 per teacher)
Angle classification
Handout (optional): Notes – Drawing an Angle
with a Protractor (1 per student)
Elaborate 2
Handout: Artistic Angles (1 per student)
Students extend their knowledge of angle measures to the construction of an angle.
Instructional Procedures:
1. Display teacher resource: Notes – Drawing an Angle with a Protractor. Demonstrate
constructing an angle for the class to see
2. Place students in groups of 4. Distribute a protractor, a ruler, and a sheet of plain paper to
each student. Instruct student pairs to draw an acute angle, an obtuse angle, and a right
MATERIALS
protractor (1 per student, 1 per teacher)
ruler (1 per student, 1 per teacher)
paper (plain) (1 sheet per student, 1 sheet per
teacher)
angle on their sheet of paper. Allow time for students to complete the activity. Monitor and
page 16 of 93 Enhanced Instructional Transition Guide
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Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Suggested Instructional Procedures
assess student pairs to check for understanding. Facilitate a class discussion on the
strategies used to draw each of the angles.
Ask:
What strategy did you use to construct the angles? (Draw a ray and put the center of
Notes for Teacher
TEACHER NOTE
Handout (optional): Notes – Drawing an Angle with
a Protractor may be used to assist struggling
students.
the protractor at the end of the ray.)
How can you verify the angle you have constructed is the correct angle
classification needed? (I can measure the constructed angle with the protractor to
determine the angle measure is correct for the classification of the angle.)
3. If time allows, instruct students to exchange papers with another group and verify each
other’s drawings using a protractor to ensure the angle constructed meets the classification
needed.
4. Distribute handout: Artistic Angles to each student as independent practice and/or
homework.
4
Topics:
Spiraling Review
Triangle classification
Engage 2
Students use logic and reasoning skills to sort a group of triangles by their attributes.
ATTACHMENTS
Card Set: Classifying Triangles (1 set per 2
students)
Instructional Procedures:
page 17 of 93 Enhanced Instructional Transition Guide
Suggested
Day
Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Suggested Instructional Procedures
1. Prior to instruction create a card set: Classifying Triangles for every 2 students by copying
Notes for Teacher
MATERIALS
on cardstock, cutting apart, and placing in a plastic zip bag.
2. Place students in pairs and distribute a card set: Classifying Triangles to each pair.
Instruct students to sort the triangles by their attributes and to discuss the characteristics of
each of their categories. Allow time for students to complete the activity. Monitor and assess
student pairs to check for understanding. Facilitate a class discussion about the
cardstock (1 sheet per 2 students)
scissors (1 per teacher)
plastic zip bag (sandwich sized) (1 per 2
students)
characteristics used to classify the triangles.
Ask:
Is there more than one way to classify triangles? (yes, by their sides or by their
angles)
What are the different angle classifications? (acute, obtuse, right, and straight)
Topics:
TEACHER NOTE
Students have classified triangles by their sides in
previous grades. The focus on classifying triangles in
Grade 6 is with angle relationships.
ATTACHMENTS
Triangle classification
Teacher Resource: Triangle Template
Triangle properties
Directions KEY (1 per teacher)
Teacher Resource: Triangle Template
Explore/Explain 4
Directions (1 per teacher)
Students discover the sum of the angles of any triangle is 180°. Students explore classifications
Handout: Triangle Template Directions (1 per
of triangles using angle classifications and the relationship between the angles of a triangle.
student)
Instructional Procedures:
MATERIALS
1. Display teacher resource: Triangle Template Directions.
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Suggested Duration: 10 days
Suggested Instructional Procedures
2. Place students in pairs. Distribute handout: Triangle Template Directions, 3 sheets of
patty paper, and a protractor to each student. Instruct students to use their patty paper to
create each triangle. Allow time for students to complete the activity. Monitor and assess
Notes for Teacher
patty paper (3 sheets per student)
protractor (1 per student)
scissors (1 per student)
student pairs to check for understanding. Facilitate a class discussion to debrief student
solutions.
TEACHER NOTE
Ask:
Students’ answers may vary when determining
In Triangle 1: What kind of angles are these? (acute)
How do you know? (they look less than 90°)
measures with a protractor. Instruct students to
measure to the nearest 5 degrees. If students do not
How can you be sure? (use a protractor to measure them)
get a sum of 180°, assure them this is due to
If you put 3 angles together and they form a straight line, what do you know
measurement error.
about the measure of the straight angle that forms the straight line? (180°)
What is the sum of the angles’ measures? (180°)
How do you know? (A straight line is formed when the angles are put together and a
State Resources
straight line forms a straight angle with a degree measure of 180°.)
How does the sum compare to your estimate? (they are both 180°)
MTR 6 – 8: Triangle Properties may be used to
For Triangle 2: What kind of angles are these? (Angles 1 and 3 are acute and angle
reinforce these concepts or as an alternate activity.
2 is obtuse.)
How do you know? (angles 1 and 3 look less than 90° and angle 2 looks greater than
90°)
How can you be sure? (use a protractor to measure them)
If you put 3 angles together and they form a straight line, what do you know
about the measure of the straight angle that forms the straight line? (180°)
What is the sum of the angles’ measures? (180°)
How do you know? (A straight line is formed when the angles are put together and a
page 19 of 93 Enhanced Instructional Transition Guide
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Unit 06:
Suggested Duration: 10 days
Notes for Teacher
straight line forms a straight angle with a degree measure of 180°.)
For Triangle 2: What kind of angles are these? (Angles 1 and 2 are acute and angle
3 is right)
How do you know? (angles 1 and 2 look less than 90° and angle 3 looks equal to 90°)
How can you be sure? (use a protractor to measure them)
If you put 3 angles together and they form a straight line, what do you know
about the measure of the straight angle that forms the straight line? (180°)
What is the sum of the angles’ measures? (180°)
How do you know? (A straight line is formed when the angles are put together and a
straight line forms a straight angle with a degree measure of 180°.)
3. Using the displayed teacher resource: Triangle Template Directions, facilitate a class
discussion about angles relationships found in triangles.
Ask:
What types of angles have you studied so far? (acute, right, straight, and obtuse)
How do you think you can use what you know about angles to classify triangles?
(I can classify them according to their angles.)
What types of angles did you find in Triangle 1? (all acute)
What do you think would be a good name for a triangle with all acute angles?
(an acute triangle)
What types of angles did you find in Triangle 2? (one obtuse and two acute)
Can you have more than one obtuse angle in a triangle? Why or why not? (No, I
can only have one obtuse and two acute.)
What do you think would be a good name for a triangle with one obtuse angle?
page 20 of 93 Enhanced Instructional Transition Guide
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Day
Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Suggested Instructional Procedures
Notes for Teacher
(an obtuse triangle)
What types of angles did you find in Triangle 3? (one right and two acute)
Can you have more than one right angle in a triangle? Why or why not? (No, you
can only have one right and two acute.)
What do you think would be a good name for a triangle with one right angle? (a
right triangle)
Would it be possible to have a “straight” triangle? (No, it is impossible to draw a
triangle with a straight angle.)
How could you find the measure of angle 2 if you only knew the measures of the
other two angles? (Add the known angles together and subtract the sum from 180°.)
4. Distribute a previously created card set: Classifying Triangles to each pair. Instruct student
pairs to sort the triangles using angle relationships. Allow time for student pairs to complete
the activity. Monitor and assess student groups to check for understanding. Facilitate a
class discussion about the triangle sorts.
5
Topics:
Spiraling Review
Triangle classifications
Triangle properties
ATTACHMENTS
Explore/Explain 5
Teacher Resource: Angle Relationships in
Students use triangle properties, classifications, and side measurements to discover side
Triangles KEY (1 per teacher)
congruency marks (tick marks). Students are introduced to the formal language of congruence,
Handout: Angle Relationships in Triangles (1
isosceles, scalene, and equilateral.
per student)
Teacher Resource: Angle Relationships in
page 21 of 93 Enhanced Instructional Transition Guide
Suggested
Day
Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Suggested Instructional Procedures
Instructional Procedures:
Notes for Teacher
Triangles (1 per teacher)
1. Place students in pairs. Distribute handout: Angle Relationships in Triangles, a protractor,
and a ruler to each student. Instruct student to complete handout with their group. Allow time
MATERIALS
for students to complete the activity. Monitor and assess student groups to check for
understanding.
protractor (1 per student)
Ask:
ruler (1 per student)
How can you measure the lengths of the sides of the triangle? (with a ruler)
How can you measure the angles of the triangle? (with a protractor)
Why do you think there are marks on the sides of the triangle? (the sides are
congruent)
What is the relationship between the angle measures and the congruency marks
on the triangles? (if the sides are congruent, then the angle opposite those sides are
congruent)
If one of the angles measure was missing, could you find the angle measure
without using a protractor? (Yes, since each triangle has a total of 180°, I can
subtract the sum of the two known angles from 180°.)
2. Display teacher resource: Angle Relationships in Triangles to facilitate a class discussion
about the relationships found between the congruency marks and the measure of the angles.
Ask:
What is a triangle called with no equal sides? (scalene)
What do you know about the angles in a scalene triangle? (there are no congruent
angles)
page 22 of 93 Enhanced Instructional Transition Guide
Suggested
Day
Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Suggested Instructional Procedures
Notes for Teacher
What is a triangle called with two or more equal sides? (isosceles)
What do you know about the angles in an isosceles triangle? (the angles opposite
the congruent sides are also congruent)
What is a triangle called with all sides congruent? (equilateral)
What do you know about the angles in an equilateral triangle? (all three angles are
also congruent)
What is another name for an equilateral triangle? (equiangular)
What markings show that sides are congruent? (tick marks or side congruency
marks)
What is the relationship between the angles and congruency marks on the sides
of a triangle? (the angles opposite the congruency marks are also congruent)
How many degrees are in a triangle? (180 degrees)
What is the measure of the angles for problem 1? (60 degrees) Why? (There are 180
degrees in a triangle, and all angles are congruent, so 180 divided by 3 is 60.)
What is the measure of the missing angles on problem 4? (45 degrees) Why?
(There are 180 degrees in a triangle; this triangle has a right angle which is 90 degrees.
180 – 90 = 90. The other two angles are congruent and equal 90 degrees together; 90
degrees divided by 2 is 45.)
Topics:
ATTACHMENTS
Triangle classifications
Teacher Resource: Missing Angle Measures
Triangle properties
in Triangles KEY (1 per teacher)
Handout: Missing Angle Measures in
Elaborate 3
Triangles (1 per student)
page 23 of 93 Enhanced Instructional Transition Guide
Suggested
Day
Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Suggested Instructional Procedures
Notes for Teacher
Students find missing angle measures in a triangle by using triangle properties and
classifications.
Instructional Procedures:
1. Place students in pairs. Distribute handout: Missing Angle Measures in Triangles to each
student. Instruct student pairs to apply their knowledge of triangle relationships to classify
and find the missing measures in each triangle. Allow time for students to complete the
activity. Monitor and assess student pairs to check for understanding. Facilitate a class
discussion to debrief student solutions.
6
Topics:
Spiraling Review
Quadrilateral properties
Explore/Explain 6
ATTACHMENTS
Students discover the sum of the angles of any quadrilateral is 360°. Students use quadrilateral
Teacher Resource: Angles Relationships in
properties to find a missing angle when given the measure of any three angles in a quadrilateral.
Quadrilaterals KEY (1 per teacher)
Handout: Angles Relationships in
Instructional Procedures:
Quadrilaterals (1 per student)
1. Place students in pairs. Distribute handout: Angle Relationships in Quadrilaterals, a
piece of patty paper, and a pair of scissors to each student.
MATERIALS
Ask:
patty paper (1 per student)
Based on what you know about triangles, what do you think will be the sum of
scissors (1 per student)
the angles of a quadrilateral? Answers may vary. 180°; 360°; etc.
protractor (1 per student)
page 24 of 93 Enhanced Instructional Transition Guide
Suggested
Day
Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Suggested Instructional Procedures
Notes for Teacher
ruler (1 per student)
2. Instruct students to trace the quadrilateral from handout: Angle Relationships in
paper (plain) (1 sheet per student)
Quadrilaterals on patty paper and cut out.
3. Instruct students to tear the corners of their cut-out quadrilateral and place them around a
common point.
State Resources
MTR 6 – 8: Creating Venn Diagrams with
Quadrilaterals and Semantic Feature Analysis Charts –
Attributes of 2-D and 3-D Figures may be used to
reinforce these concepts or as an alternate activity.
TEACHER NOTE
The teacher may choose to use the symbol for
Ask:
congruent and record the following beside the
What is the sum of the angles of a quadrilateral? (360°)
parallelogram:
How do you know? Answers may vary. There are two straight angles; etc.
If two segments have the same measure, the
How can you verify the sum of the angles of the quadrilateral? (measure the angles
segments are congruent segments. If two angles have
with a protractor and add the measures)
the same measure, the angles are congruent angles.
The symbol used to represent congruence is . Based
4. Distribute a protractor, ruler, and sheet of plain paper to each student. Instruct students to
on the markings made on parallelogram ABCD, the
measure the angles and sides of the quadrilateral from handout: Angle Relationships in
following congruence statements can be
Quadrilaterals and record their findings in the table.
written:
5. Instruct students to draw and label 3 quadrilaterals on their sheet of paper: Quadrilateral 2 –
a parallelogram, Quadrilateral 3 – a rectangle, Quadrilateral 4 – a trapezoid .Then, record the
page 25 of 93 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Notes for Teacher
measure of each angle and the length of each side in the table on their handout: Angle
Relationships in Quadrilaterals. Allow time for students to complete the activity. Monitor
and assess student groups to check for understanding. Facilitate a class discussion about
relationships of quadrilaterals.
Ask:
What did you discover about the sum of the angles of a quadrilateral? (The sum is
360°.)
Can you have more than one obtuse angle in a quadrilateral? (yes)
Can you have more than one right angle in a quadrilateral? (yes)
Can you have more than one acute angle in a quadrilateral? (yes)
Can you have more than two obtuse angles in a quadrilateral? (no)
Can you have four acute angles in a quadrilateral? (no)
Can you have four right angles in a quadrilateral? (yes)
If you know the measures of three angles in a quadrilateral, could you find the
measure of the missing angle? (yes) How? (sum the other 3 angles and subtract the
sum from 360°)
When lengths are the same measure you say they are congruent. Did you find
any congruent angles in your parallelogram? (yes, opposite angles)
Could you prove this? (yes, by measuring the lengths of the sides and measure the
opposite angles)
Did you find any congruent angles in your rectangle? (Yes, all the angles are right
angles.)
6. Display the following parallelogram for the class to see.
page 26 of 93 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Notes for Teacher
Ask:
Which of these sides are congruent? (opposite sides)
Which of these angles are congruent? (opposite angles)
How many degrees are in a parallelogram? (360°)
How many degrees are in half a parallelogram? (180°)
7. Draw the following square for the class to see.
Ask:
Which of these sides are congruent? (all sides)
Which of these angles are congruent? (all angles)
If the sum of the angles is 360° and all the angles are congruent, what is the
measure of each angle? Justify your response. (360° ÷ 4 = 90°)
How would you classify the angles in the square? (right angles)
When all the sides are congruent and all the angles are congruent in a polygon,
page 27 of 93 Enhanced Instructional Transition Guide
Suggested
Day
Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Suggested Instructional Procedures
Notes for Teacher
it is called a regular polygon. Which of the triangles you discussed would be
considered regular? (equilateral)
How do you know? (all the sides are congruent and all the angles are congruent)
How can you determine whether or not a polygon is a regular polygon? (measure
the sides and angles to determine if they are congruent or not)
7
Topics:
Spiraling Review
Quadrilateral classifications
Quadrilateral properties
ATTACHMENTS
Elaborate 4
Teacher Resource: Missing Angle Measures
Students use quadrilateral properties and classifications to find missing angle measures in
in Quadrilaterals KEY (1 per teacher)
quadrilaterals.
Handout: Missing Angle Measures in
Quadrilaterals (1 per student)
Instructional Procedures:
1. Place students in pairs. Distribute handout: Missing Angle Measures in Quadrilaterals to
each student. Instruct student pairs to apply their knowledge of quadrilateral relationships to
classify and find the missing measures in each quadrilateral. Allow time for students to
complete the activity. Monitor and assess student pairs to check for understanding.
Facilitate a class discussion to debrief student solutions.
page 28 of 93 Enhanced Instructional Transition Guide
Suggested
Day
8 – 9
Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Suggested Instructional Procedures
Notes for Teacher
Topics:
Spiraling Review
Triangle properties
Quadrilateral properties
ATTACHMENTS
Elaborate 5
Teacher Resource: Sum of Angles KEY (1 per
Students extend their knowledge of the properties of triangles and quadrilaterals to find missing
teacher)
angle measurements and classify triangles and quadrilaterals.
Handout: Sum of Angles (1 per student)
Teacher Resource: Polygon Angle Evaluation
Instructional Procedures:
1. Prior to instruction create a class resource: I Have, Who Has? for every teacher by copying
on cardstock, cutting apart, and placing in a plastic zip bag.
KEY (1 per teacher)
Handout: Polygon Angle Evaluation (1 per
student)
Card Set: I Have, Who Has? (1 per teacher)
2. Place students in pairs and distribute handout: Sum of Angles to each student. Instruct
student pairs to find all the missing angle measures. Allow time for students to complete the
activity. Monitor and assess student pairs to check for understanding. Facilitate a class
discussion to debrief student solutions, as needed.
3. Distribute handout: Polygon Angle Evaluation to each student. Instruct students to
independently solve each problem by applying concepts of triangle and quadrilateral
MATERIALS
cardstock (7 sheets per teacher)
scissors (1 per teacher)
plastic zip bag (sandwich sized) (1 per teacher)
relationships. Allow time for students to complete the activity. Monitor and assess students
to check for understanding. Facilitate a class discussion to debrief student solutions, as
needed.
State Resources
4. Distribute a card from card set: “I Have, Who Has?” to each student. Instruct any student to
start the game. The first student will ask the “Who has?” question from the bottom of the
MTR 6 – 8: Can You Describe Me? may be used to
page 29 of 93 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
card. The student who has the matching answer will answer “I have…” and read the top of the
Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Notes for Teacher
reinforce these concepts or as an alternate activity.
card. The answering student will then read the “Who has?” section of the card and continue
the process until the first student reads the “I have” section of the original card.
10
Evaluate 1
Instructional Procedures:
1. Assess student understanding of related concepts and processes by using the Performance
Indicator(s) aligned to this lesson.
Performance Indicator (s):
Grade6 Mathematics Unit06 PI01
Use a drawing of a triangle or quadrilateral to find each angle measurement and classification.
Generate a model (e.g., sketch, computer-generated, etc.) of the drawing, and label the angle
measure using measurement notation and the classification (e.g., acute, obtuse, or right) for each
angle. Validate each measure by explaining the angle relationships and problem-solving
processes.
Sample Performance Indicator:
A government surveyor provided the following diagram of the new city park
land. Sketch the diagram, and label the angle measure using measurement
notation and the classification for each angle. Justify each measure by
explaining the angle relationships and problem-solving processes.
page 30 of 93 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 6/Mathematics
Unit 06:
Suggested Duration: 10 days
Notes for Teacher
Standard(s): 6.6A , 6.6B , 6.8C , 6.11B , 6.11C , 6.11D , 6.13A , 6.13B
ELPS ELPS.c.1C , ELPS.c.3H
04/24/13
page 31 of 93 Grade 6
Mathematics
Unit: 06 Lesson: 01
What’s My Angle? KEY
©2012, TESCCC
acute
obtuse
straight
right
straight
obtuse
acute
acute
acute
right
obtuse
09/19/12
obtuse
page 1 of 1
Grade 6
Mathematics
Unit: 06 Lesson: 01
What’s My Angle?
©2012, TESCCC
09/19/12
page 1 of 1
Grade 6
Mathematics
Unit: 06 Lesson: 01
What’s My Angle Measure? KEY
Use a protractor to measure each angle. Use the angle measure to classify each angle.
Angle
Angle Measure
Angle Classification
1.
90°
right
50°
acute
170°
obtuse
45°
acute
120°
obtuse
2.
3.
4.
5.
©2012, TESCCC
09/19/12
page 1 of 1
Grade 6
Mathematics
Unit: 06 Lesson: 01
What’s My Angle Measure?
Use a protractor to measure each angle. Use the angle measure to classify each angle.
Angle
Angle Measure
Angle Classification
1.
2.
3.
4.
5.
©2012, TESCCC
09/19/12
page 1 of 1
Grade 6
Mathematics
Unit: 06 Lesson: 01
Measuring with a Protractor KEY
Record the angle measure for each angle and state whether the angle is acute, right, obtuse, or
straight.
1.
2.
Angle Measure 130° Angle Classification
obtuse
Angle Measure 100° Angle Classification
obtuse
3.
4.
Angle Measure 90° Angle Classification right
5.
Angle Measure 180° Angle Classification
straight
6.
Angle Measure 85° Angle Classification acute
Angle Measure 85° Angle Classification acute
©2012, TESCCC
04/24/13
page 1 of 2
Grade 6
Mathematics
Unit: 06 Lesson: 01
Measuring with a Protractor KEY
Record the angle measure for each angle and state whether the angle is acute, right, obtuse, or
straight.
7.
8.
Angle Measure 140° Angle Classification
obtuse
Angle Measure 90° Angle Classification right
9.
10.
Angle Measure 20° Angle Classification acute
Angle Measure 135° Angle Classification
obtuse
11.
12.
Angle Measure 180° Angle Classification
straight
Angle Measure 95° Angle Classification obtuse
©2012, TESCCC
04/24/13
page 2 of 2
Grade 6
Mathematics
Unit: 06 Lesson: 01
Measuring with a Protractor
Record the angle measure for each angle and state whether the angle is acute, right, obtuse, or
straight.
1.
2.
Angle Measure _____ Angle Classification ____
Angle Measure _____ Angle Classification ____
3.
4.
Angle Measure _____ Angle Classification ____
Angle Measure ____ Angle Classification ____
5.
6.
Angle Measure ____ Angle Classification ____
Angle Measure ____ Angle Classification _____
©2012, TESCCC
04/24/13
page 1 of 2
Grade 6
Mathematics
Unit: 06 Lesson: 01
Measuring with a Protractor
Record the angle measure for each angle and state whether the angle is acute, right, obtuse, or
straight.
7.
8.
Angle Measure ____ Angle Classification
______
Angle Measure ____ Angle Classification _____
9.
10.
Angle Measure ____ Angle Classification
______
Angle Measure ____ Angle Classification _____
11.
12.
Angle Measure ____ Angle Classification
______
Angle Measure ____ Angle Classification______
©2012, TESCCC
04/24/13
page 2 of 2
Grade 6
Mathematics
Unit: 06 Lesson: 01
How Many Degrees? KEY
•
•
•
1)
3)
Classify each angle as acute, obtuse, right, or straight.
Estimate the measure of each angle.
Estimates may vary.
Measure the angle and record the measure of the angle.
Angle Classification: Acute
2)
Angle Classification: Acute
Estimated Measure: 70°
Estimated Measure: 90°
Angle Measure: 65°
Angle Measure: 90°
Angle Classification: Acute
4)
Angle Classification: Right
Estimated Measure: 50°
Estimated Measure: 90°
Angle Measure: 48°
Angle Measure: 90°
©2012, TESCCC
04/24/13
page 1 of 3
Grade 6
Mathematics
Unit: 06 Lesson: 01
How Many Degrees? KEY
•
•
•
5)
7)
Classify each angle as acute, obtuse, right, or straight.
Estimate the measure of each angle.
Estimates may vary.
Measure the angle and record the measure of the angle.
Angle Classification: Straight
6)
Angle Classification: Obtuse
Estimated Measure: 180°
Estimated Measure: 130°
Angle Measure: 180°
Angle Measure: 145°
Angle Classification: Obtuse
8)
Angle Classification: Acute
Estimated Measure: 130°
Estimated Measure: 80°
Angle Measure: 115°
Angle Measure: 76°
©2012, TESCCC
04/24/13
page 2 of 3
Grade 6
Mathematics
Unit: 06 Lesson: 01
How Many Degrees? KEY
•
•
•
Measure and record the measure of each angle in the polygon.
Estimate the perimeter of the polygon to the nearest centimeter.
Measure the length of each side of the polygon to the nearest centimeter and calculate the
perimeter.
9) Estimated Perimeter:
Answers will vary. Look for reasonable responses from students for angle measures and side
length measures.
For example: measure of angle A = 90°
measure of angle B = 35° to 40°
measure of angle C = 50° to 55°
Address any student responses that are not reasonable to the sample estimates above.
Calculated Perimeter:
3 cm + 4 cm + 5 cm = 12 cm
C
53°
5 cm
3 cm
90°
A
37°
4 cm
B
10) What tool did you use to measure the angles in the polygon? What unit of measure did you use to
record the measure of each angle?
Answer: protractor with units of degrees.
11) What tool did you use to measure the length of each side of the polygon? What unit of measure
did you use to record the length of each side of the polygon?
Answer: ruler with units of centimeters
©2012, TESCCC
04/24/13
page 3 of 3
Grade 6
Mathematics
Unit: 06 Lesson: 01
How Many Degrees?
•
•
•
Classify each angle as acute, obtuse, right, or straight.
Estimate the measure of each angle.
Measure the angle and record the measure of the angle.
1) Angle Classification:
3)
2)
Angle Classification:
Estimated Measure:
Estimated Measure:
Angle Measure:
Angle Measure:
Angle Classification:
4)
Angle Classification:
Estimated Measure:
Estimated Measure:
Angle Measure:
Angle Measure:
©2012, TESCCC
04/24/13
page 1 of 3
Grade 6
Mathematics
Unit: 06 Lesson: 01
How Many Degrees?
•
•
•
Classify each angle as acute, obtuse, right, or straight.
Estimate the measure of each angle.
Measure the angle and record the measure of the angle.
5) Angle Classification:
6) Angle Classification:
Estimated Measure:
Estimated Measure:
Angle Measure:
Angle Measure:
7) Angle Classification:
8) Angle Classification:
Estimated Measure:
Estimated Measure:
Angle Measure:
Angle Measure:
©2012, TESCCC
04/24/13
page 2 of 3
Grade 6
Mathematics
Unit: 06 Lesson: 01
How Many Degrees?
•
•
•
Measure and record the measure of each angle in the polygon.
Estimate the perimeter of the polygon to the nearest centimeter.
Measure the length of each side of the polygon to the nearest centimeter and calculate the
perimeter.
9) Estimated Perimeter:
Calculated Perimeter:
C
A
B
10) What tool did you use to measure the angles in the polygon? What unit of measure did you use to
record the measure of each angle?
11) What tool did you use to measure the length of each side of the polygon? What unit of measure
did you use to record the length of each side of the polygon?
©2012, TESCCC
04/24/13
page 3 of 3
Grade 6
Mathematics
Unit: 06 Lesson: 01
Naming Angles KEY
A) There are three ways to name an angle. The symbol “ ∠ ” stands for angle.
•
3 letters may be used to name an angle. Name all the angles in Figure 1 below.
Figure 1
∠
∠
∠
Answer: ∠ BAC or ∠ CAB; ∠ BAD or ∠ DAB; ∠ BAE or ∠ EAB; ∠ BAF or FAB; ∠ CAD or
∠ DAC; ∠ CAE or ∠ EAC; ∠ CAF or ∠ FAC; ∠ DAE or ∠ EAD; ∠ DAF or ∠ FAD; ∠ EAF or
∠ FAE
• 1 letter (the vertex letter of an angle) may be used to name an angle. Use one letter to name
the angles in Figure 2 below.
Figure 2
Answer: ∠ Y; ∠ D; ∠ A; ∠ B; ∠ C
• A number may be used to name an angle. Use numbers to name the angles in Figure 3 below.
Figure 3
Answer: ∠ 1; ∠ 2; ∠ 3; ∠ 4; ∠ 5
B) Angles are measured in degrees. The symbol “°” stands for degrees. A lower case “m” is written in
front of the angle symbol ( ∠ ) to indicate the degree measure of an angle. Use Figure 1 and write
the measure of ∠ EAF, ∠ DAF, and ∠ CAF. Refer to Figure 1 for the angle measurements. The
teacher will model measuring the angles with a protractor and write the measures in the diagram.
©2012, TESCCC
09/19/12
page 1 of 1
Grade 6
Mathematics
Unit: 06 Lesson: 01
Naming Angles
A) There are three ways to name an angle. The symbol “  ” stands for angle.

3 letters may be used to name an angle. Name all the angles in Figure 1 below.
Figure 1
D
C
E
B

F
A
1 letter (the vertex letter of an angle) may be used to name an angle. Use one letter to name
the angles in Figure 2 below.
Figure 2
C
Z
X

Y
D
A
B
A number may be used to name an angle. Use numbers to name the angles in Figure 3 below.
Figure 3
B) Angles are measured in degrees. The symbol “°” stands for degrees. A lower case “m” is written in
front of the angle symbol (  ) to indicate the degree measure of an angle. Use Figure 1 and write
the measure of  EAF,  DAF, and  CAF.
©2012, TESCCC
09/18/12
page 1 of 1
Grade 6
Mathematics
Unit: 06 Lesson: 01
Notes – Drawing an Angle with a Protractor
1. Draw a ray and label it.
A
B
2. Place the vertex of the protractor on the
endpoint of the ray. Line up the ray with the 0°
mark.
A
3. Using the scale with the 0° mark, find the
measure of the angle you wish to draw (use
150°). Place a pencil mark on that degree
measure to “keep your place” when you lift
the protractor to draw this ray.
B
Pencil Mark
A
4. Move the protractor out of the way, and use
the straightedge of the protractor to draw the
other ray. Label the other point on this ray.
B
C
A
B
5. Use your protractor to draw and label an acute, obtuse, right, and straight angle.
©2012, TESCCC
09/18/12
page 1 of 1
Grade 6
Mathematics
Unit: 06 Lesson: 01
Artistic Angles
Students should have paper, protractors, and rulers to complete these tasks.
Task 1
Draw a house that has one acute angle and one obtuse angle. Use your protractor to measure and
label each angle.
Task 2
Draw a skateboard with two straight angles and two right angles. Use your protractor to measure and
label each angle.
©2012, TESCCC
09/19/12
page 1 of 1
Grade 6
Mathematics
Unit: 06 Lesson: 01
Classifying Triangles
C
A
B
M
S
©2012, TESCCC
L
09/19/12
page 1 of 1
Grade 6
Mathematics
Unit: 06 Lesson: 01
Triangle Template Directions KEY
Follow the directions below using Triangle 1.
1) Trace Triangle 1 on a piece of patty
paper. Label the each of angles 1, 2,
and 3 like Triangle 1 to the right.
1
Triangle 1
2) Tear off each angle from the traced
Triangle 1 as shown in the diagram.
2
3) Line up and piece the 3 angles
together so the three vertices are
touching at the same point. Refer to
the diagram at the right.
3
1
2
3
4) Estimate each angle measure and
the sum of the 3 angles.
m  1 + m  2 + m  3 = 180°
5) Classify each angle.
 1 – acute ,  2 – acute,  3 – acute
6) Use a protractor and measure each
of the 3 angles. Record the measure
of each angle.
m  1 = 60°; m  2 = 60°; m  3 = 60°
7) What is the sum of the 3 angle
measures? How does the sum
compare to your estimate in step 4?
180°; it is the same value as the estimate
©2012, TESCCC
09/18/12
page 1 of 4
Grade 6
Mathematics
Unit: 06 Lesson: 01
Triangle Template Directions KEY
Follow the directions below using Triangle 2.
8) Trace Triangle 2 on a piece of patty
paper. Label the each of angles 1, 2,
and 3 like Triangle 2 to the right.
Triangle 2
9) Tear off each angle from the traced
Triangle 2.
10) Line up and piece the 3 angles
together so the three vertices are
touching at the same point. Refer to
the diagram at the right.
1
2
3
11) Estimate each angle measure and
the sum of the 3 angles.
m  1 + m  2 + m  3 = 180°
12) Classify each angle.
 1 – acute ,  2 – obtuse,  3 – acute
13) Use a protractor and measure each
of the 3 angles. Record the measure
of each angle.
m  1 = 25°; m  2 = 130°; m  3 = 25°
14) What is the sum of the 3 angle
measures? How does the sum
compare to your estimate in step 4?
180°, it is the same value as the estimate
©2012, TESCCC
09/18/12
page 2 of 4
Grade 6
Mathematics
Unit: 06 Lesson: 01
Triangle Template Directions KEY
Follow the directions below using Triangle 3.
15) Trace Triangle 3 on a piece of patty
paper. Label the each of angles 1, 2,
and 3 like Triangle 3 to the right.
1
Triangle 3
16) Tear off each angle from the traced
Triangle 3.
3
2
17) Line up and piece the 3 angles
together so the three vertices are
touching at the same point. Refer to
the diagram at the right.
1
2
3
18) Estimate each angle measure and
the sum of the 3 angles.
m  1 + m  2 + m  3 = 180°
19) Classify each angle.
 1 – acute ,  2 – acute,  3 – right
20) Use a protractor and measure each
of the 3 angles. Record the measure
of each angle.
m  1 = 35°; m  2 = 55°; m  3 = 90°
21) What is the sum of the 3 angle
measures? How does the sum
compare to your estimate in step 4?
180° is the same value as the estimate
©2012, TESCCC
09/18/12
page 3 of 4
Grade 6
Mathematics
Unit: 06 Lesson: 01
Triangle Template Directions KEY
Record the estimated and the actual angle measures from Triangle 1, Triangle 2, and Triangle 3 in the
table below.
Triangle
Estimated Sum
of Angle
Measures
Angle
Measures
Actual Sum of
Angle
Measures
m 1 =60
1
60° + 60° + 60° =
180°
m 2 =60
180
m 3 =60
m 1 =25
2
30° + 30° + 120° =
180°
m 2 =130
180
m 3 =25
m 1 =35
3
40° + 50° + 90° =
180°
m 2 =55
180
m 3 =90
22) What does the data in your table tell you about the sum of the angle measures in a triangle?
Explain.
The sum of the angles of a triangle is 180 degrees.
©2012, TESCCC
09/18/12
page 4 of 4
Grade 6
Mathematics
Unit: 06 Lesson: 01
Triangle Template Directions
Follow the directions below using Triangle 1.
1) Trace Triangle 1 on a piece of patty
paper. Label the each of angles 1, 2,
and 3 like Triangle 1 to the right.
1
Triangle 1
2) Tear off each angle from the traced
Triangle 1 as shown in the diagram.
2
3) Line up and piece the 3 angles
together so the three vertices are
touching at the same point. Refer to
the diagram at the right.
3
1
2
3
4) Estimate each angle measure and
the sum of the 3 angles.
5) Classify each angle.
6) Use a protractor and measure each
of the 3 angles. Record the measure
of each angle.
7) What is the sum of the 3 angle
measures? How does the sum
compare to your estimate in step 4?
©2012, TESCCC
09/18/12
page 1 of 4
Grade 6
Mathematics
Unit: 06 Lesson: 01
Triangle Template Directions
Follow the directions below using Triangle 2.
8) Trace Triangle 2 on a piece of patty
paper. Label the each of angles 1, 2,
and 3 like Triangle 2 to the right.
Triangle 2
9) Tear off each angle from the traced
Triangle 2.
10) Line up and piece the 3 angles
together so the three vertices are
touching at the same point. Refer to
the diagram at the right.
1
2
3
11) Estimate each angle measure and
the sum of the 3 angles.
12) Classify each angle.
13) Use a protractor and measure each
of the 3 angles. Record the measure
of each angle.
14) What is the sum of the 3 angle
measures? How does the sum
compare to your estimate in step 4?
©2012, TESCCC
09/18/12
page 2 of 4
Grade 6
Mathematics
Unit: 06 Lesson: 01
Triangle Template Directions
Follow the directions below using Triangle 3.
15) Trace Triangle 3 on a piece of patty
paper. Label the each of angles 1, 2,
and 3 like Triangle 3 to the right.
1
Triangle 3
16) Tear off each angle from the traced
Triangle 3.
3
2
17) Line up and piece the 3 angles
together so the three vertices are
touching at the same point. Refer to
the diagram at the right.
1
2
3
18) Estimate each angle measure and
the sum of the 3 angles.
19) Classify each angle.
20) Use a protractor and measure each
of the 3 angles. Record the measure
of each angle.
21) What is the sum of the 3 angle
measures? How does the sum
compare to your estimate in step 4?
©2012, TESCCC
09/18/12
page 3 of 4
Grade 6
Mathematics
Unit: 06 Lesson: 01
Triangle Template Directions
Record the estimated and the actual angle measures from Triangle 1, Triangle 2, and Triangle 3 in
the table below.
Triangle
Estimated Sum
of Angle
Measures
Angle
Measures
Actual Sum of
Angle
Measures
m 1 =
1
m 2 =
m 3 =
m 1 =
2
m 2 =
m 3 =
m 1 =
3
m 2 =
m 3 =
1) What does the data in your table tell you about the sum of the angle measures in a triangle?
Explain.
©2012, TESCCC
09/18/12
page 4 of 4
Grade 6
Mathematics
Unit: 06 Lesson: 01
Angle Relationships in Triangles KEY
Measure each side with a ruler and record your measurement.
1.
2.
1 in.
2
2
7
8
3.
1
in.
8
1
in.
16
4.
5
8
3
4
5
8
1
4
5
8
5. What do you think the tick marks on the sides of the triangles represent? Answers may vary.
6. Measure each angle with a protractor and record you angle measure.
Triangle in Problem 1: 45° – 45° – 90°; Triangle in Problem 2: 62° – 36° – 82°;
Triangle in Problem 3: 60° – 60° – 60°; Triangle in Problem 4: 37° – 53° – 90°
7. What is the relationship between the angle measures and the congruency marks on the sides of
the triangle?
The number of congruency marks denote the number of congruent angles. If the sides are
congruent, then the angles opposite those sides are congruent.
©2012, TESCCC
09/18/12
page 1 of 1
Grade 6
Mathematics
Unit: 06 Lesson: 01
Angle Relationships in Triangles
Measure each side with a ruler and record your measurement.
1.
2.
3.
4.
5. What do you think the tick marks on the sides of the triangles represent?
6. Measure each angle with a protractor and record you angle measure.
7. What is the relationship between the angle measures and the congruency marks on the sides of
the triangle?
©2012, TESCCC
09/19/12
page 1 of 1
Grade 6
Mathematics
Unit: 06 Lesson: 01
Missing Angle Measures in Triangles KEY
Measure the triangle side length and find the missing angle measures for each triangle. Show your
work.
1.
2.
C
H
D
63º
I 121º
35º
31º
E
m∠C = 82°
m∠H = 28°
Classification: acute scalene
Classification: obtuse scalene
3.
4.
X
A
Y
B
J
55º
Z
C
m∠A = 45°
m∠X = 70°
m∠B = 90°
m∠Z = 55°
m∠C = 45°
Classification: right isosceles
©2012, TESCCC
Classification: acute isosceles
04/24/13
page 1 of 2
Grade 6
Mathematics
Unit: 06 Lesson: 01
Missing Angle Measures in Triangles KEY
Measure the triangle side length and find the missing angle measures for each triangle. Show your
work.
5.
6.
Q
F
78º
38º
G
R
H
S
m∠Q = 60°
m∠F = 40°
m∠R = 60°
m∠FGH = 102°
m∠S = 60°
Classification: equilateral (equiangular)
7.
Classification: obtuse scalene
8.
L
A
46º
B
50º
87º
M
m∠M = 65°
C
m∠C = 47°
m∠N = 65°
Classification: acute scalene
Classification: acute isosceles
©2012, TESCCC
N
04/24/13
page 2 of 2
Grade 6
Mathematics
Unit: 06 Lesson: 01
Missing Angle Measures in Triangles
Missing the triangle side lengths and find the missing angle measures for each triangle. Show your
work.
1.
2.
C
D
H
63º
I 121º
35º
E
Classification:
3.
Classification:
4.
A
m∠A = _____________
m∠B = _____________
m∠C = _____________
Classification:
©2012, TESCCC
J
m∠H = _____________
m∠C = _____________
B
31º
X
Y
C
55º
Z
m∠X = _____________
m∠Z = _____________
Classification:
04/24/13
page 1 of 2
Grade 6
Mathematics
Unit: 06 Lesson: 01
Missing Angle Measures in Triangles
Measure the triangle side length and find the missing angle measures for each triangle. Show your
work.
5.
6.
Q
F
78º
38º
G
R
H
S
m∠F = _____________
m∠Q = _____________
m∠FGH = _____________
m∠R = _____________
m∠S = _____________
Classification:
8.
Classification:
7.
L
A
46º
B
50º
87º
M
m∠M = _____________
C
m∠C = _____________
m∠N = _____________
Classification:
Classification:
©2012, TESCCC
N
04/24/13
page 2 of 2
Grade 6
Mathematics
Unit: 06 Lesson: 01
Angle Relationships in Quadrilaterals KEY
1) Trace the quadrilateral below (Quadrilateral 1) and cut it out.
2
3
1
4
2) Tear off the corners of the figure.
2
3
1
4
3) Place them together around a common point as shown.
1
2
4
3
4) What is the sum of the four angles? Justify your response.
360, measure with a protractor or estimate visually
©2012, TESCCC
09/18/12
page 1 of 3
Grade 6
Mathematics
Unit: 06 Lesson: 01
Angle Relationships in Quadrilaterals KEY
5) Draw three other quadrilaterals. Make one a parallelogram (Quadrilateral 2), one a rectangle
(Quadrilateral 3), and one a trapezoid (Quadrilateral 4). Record the measure of each angle and
the length of each side opposite the angle in the table below.
Quadrilateral
1
Angle Measures
Side
m 1 =65
6 cm
m 2 =120
8 cm
m 3 =100
6.5 cm
m 4 =75
13 cm
Sum =360
m 1 =
m 2 =
2
m 3 =
m 4 =
Sum =
m 1 =
m 2 =
3
m 3 =
m 4 =
Sum =
m 1 =
m 2 =
4
m 3 =
m 4 =
Sum =
©2012, TESCCC
09/18/12
page 2 of 3
Grade 6
Mathematics
Unit: 06 Lesson: 01
Angle Relationships in Quadrilaterals KEY
6) Based on the information in this table, what can you conclude about the sum of the angles in all of
the quadrilaterals?
The sum of the measures of the angles in a quadrilateral is equal to 360.
7) Based on the information in this table, what can you say about the sides and angles of a
rectangle, parallelogram, and trapezoid?
Rectangle: A four sided polygon (quadrilateral) with four right angles (90). Adjacent sides are
perpendicular. Opposite sides are congruent and parallel.
Parallelogram: Quadrilateral with both pair of opposite sides parallel. Opposite angles are
congruent. Opposite sides are congruent.
Trapezoid: Quadrilateral with exactly one pair of parallel sides.
©2012, TESCCC
09/18/12
page 3 of 3
Grade 6
Mathematics
Unit: 06 Lesson: 01
Angle Relationships in Quadrilaterals
1) Trace the quadrilateral below (Quadrilateral 1) and cut it out.
2
3
1
4
2) Tear off the corners of the figure.
2
3
1
4
3) Place them together around a common point.
4) What is the sum of the four angles? Justify your response.
©2012, TESCCC
09/18/12
page 1 of 3
Grade 6
Mathematics
Unit: 06 Lesson: 01
Angle Relationships in Quadrilaterals
5) Draw three other quadrilaterals. Make one a parallelogram (Quadrilateral 2), one a rectangle
(Quadrilateral 3), and one a trapezoid (Quadrilateral 4). Record the measure of each angle and
the length of each side opposite the angle in the table below.
Quadrilateral
Angle Measures
Side
m 1 =
m 2 =
1
m 3 =
m 4 =
Sum =
m 1 =
m 2 =
2
m 3 =
m 4 =
Sum =
m 1 =
m 2 =
3
m 3 =
m 4 =
Sum =
m 1 =
m 2 =
4
m 3 =
m 4 =
Sum =
©2012, TESCCC
09/18/12
page 2 of 3
Grade 6
Mathematics
Unit: 06 Lesson: 01
Angle Relationships in Quadrilaterals
6) Based on the information in this table, what can you conclude about the sum of the angles in all
of the quadrilaterals?
7) Based on the information in this table, what can you say about the sides and angles of a
rectangle, parallelogram, and trapezoid?
©2012, TESCCC
09/18/12
page 3 of 3
Grade 6
Mathematics
Unit: 06 Lesson: 01
Missing Angle Measures in Quadrilaterals KEY
Find the missing angle measures for each quadrilateral. Show your work.
1.
2.
E
D
K
75º
F
M
105º
G
55º
140º
L
105º
N
m∠E = 75°
m∠M = 60°
m∠F = 105°
Classification: quadrilateral
4.
Classification: trapezoid
3.
Q
A
B
130º
30º
R
130º
C
S
D
T
m∠R = 150°
m∠A = 50°
m∠S = 90°
m∠D = 50°
m∠T = 90°
Classification: rhombus
Classification: trapezoid
©2012, TESCCC
01/21/13
page 1 of 2
Grade 6
Mathematics
Unit: 06 Lesson: 01
Missing Angle Measures in Quadrilaterals KEY
Find the missing angle measures for each quadrilateral. Show your work.
5.
6.
T
I
H
U
V
50º
J
S
m∠S = 90°
m∠T = 90°
m∠U = 90°
m∠V = 90°
K
m∠H = 130°
m∠I = 50°
m∠K = 130°
Classification: square
Classification: parallelogram
8.
7.
C
E
D
F
m∠C = 90°
m∠D = 90°
m∠E = 90°
m∠F = 90°
Classification: rectangle
©2012, TESCCC
O
P
65º
R
Q
m∠O = 65°
m∠P = 115°
m∠Q = 115°
m∠R = 65°
Classification: parallelogram
01/21/13
page 2 of 2
Grade 6
Mathematics
Unit: 06 Lesson: 01
Missing Angle Measures in Quadrilaterals
Find the missing angle measures for each quadrilateral. Show your work.
1.
2.
E
D
K
75º
F
M
105º
G
55º
140º
L
105º
N
m∠E = ___________
m∠M = ___________
m∠F = ___________
Classification:
4.
Classification:
3.
Q
A
B
130º
30º
R
130º
C
S
D
T
m∠R = ___________
m∠A = ___________
m∠S = ___________
m∠D = ___________
m∠T = ___________
Classification:
Classification:
©2012, TESCCC
01/21/13
page 1 of 2
Grade 6
Mathematics
Unit: 06 Lesson: 01
Missing Angle Measures in Quadrilaterals
Find the missing angle measures for each quadrilateral. Show your work.
5.
6.
T
I
H
U
V
50º
J
S
m∠S = _________
m∠T = ________
m∠U = _________
m∠V = _________
K
m∠H = ___________
m∠I = ___________
m∠K = ___________
Classification:
Classification:
8.
7.
C
E
D
O
F
m∠C = _________
m∠D = _________
m∠E = _________
m∠F = _________
Classification:
©2012, TESCCC
P
65º
Q
R
m∠O = _________
m∠P = ________
m∠Q = _________
m∠R = _________
Classification:
01/21/13
page 2 of 2
Grade 6
Mathematics
Unit: 06 Lesson: 01
Sum of Angles KEY
Directions: Find all missing angle measures. Add all the measures for each figure and
write the sum inside of the figure. Show work to support your answers! Quadrilateral
ABCD and Quadrilateral PRST are parallelograms.
Angle
a
Measure 90˚
b
125˚
c
90˚
d
57˚
e
70˚
f
70˚
g
h
110˚ 95˚
j
135˚
k
135˚
m
45˚
n
151˚
a
180o
B
360o
b
C
g
f
d
360o
A
180o
110°
e
c
33°
D
180o
360o
h
j
k
m
360o
n
©2012, TESCCC
09/18/12
page 1 of 1
Grade 6
Mathematics
Unit: 06 Lesson: 01
Sum of Angles
Directions: Find all missing angle measures. Add all the measures for each figure and
write the sum inside of the figure. Show work to support your answers! Quadrilateral
ABCD and Quadrilateral PRST are parallelograms.
Angle
a
Measure
b
c
d
e
f
g
h
j
k
m
n
a
b
C
B
g
f
A
d
110°
e
c
33°
D
k
h
j
m
n
©2012, TESCCC
09/18/12
page 1 of 1
Grade 6
Mathematics
Unit: 06 Lesson: 02
I Have, Who Has?
I have:
Who has:
I have:
Who has:
I have:
Who has:
©2012, TESCCC
Parallel lines
Lines that intersect at right
angles (90 degrees) to each
other
Perpendicular lines
Figure having only two
dimensions, especially
length and width
Two-dimensional figure
Closed figure made by
joining line segments,
where each line segment
intersects exactly two
others at endpoints
09/19/12
page 1 of 7
Grade 6
Mathematics
Unit: 06 Lesson: 02
I Have, Who Has?
I have:
Polygon
Regular
Who has:
Any 4-sided polygon
I have:
Who has:
Irregular
Quadrilateral
Quadrilateral with
 opposite sides parallel
 opposite sides congruent
I have:
Parallelogram
Who has:
Quadrilateral with
 4 right (90º) angles
 adjacent sides
perpendicular
 opposite sides congruent
 opposite sides parallel
©2012, TESCCC
09/19/12
page 2 of 7
Grade 6
Mathematics
Unit: 06 Lesson: 02
I Have, Who Has?
I have:
Who has:
I have:
Rectangle
Quadrilateral with
 all sides congruent
 opposite sides are parallel
 4 right (90º) angles
 adjacent sides
perpendicular
Square
Who has:
Quadrilateral with
 all sides congruent
 opposite sides parallel
I have:
Rhombus
Who has:
©2012, TESCCC
Quadrilateral with
 exactly one pair of
parallel sides
09/19/12
page 3 of 7
Grade 6
Mathematics
Unit: 06 Lesson: 02
I Have, Who Has?
I have:
Trapezoid
Who has:
I have:
Polygon with
 3 sides
 3 angles
 3 vertices
Triangle
Polygon with
 5 sides
 5 angles
 5 vertices
Who has:
I have:
Pentagon
Who has:
©2012, TESCCC
Polygon with
 6 sides
 6 angles
 6 vertices
09/19/12
page 4 of 7
Grade 6
Mathematics
Unit: 06 Lesson: 02
I Have, Who Has?
I have:
Who has:
I have:
Who has:
I have:
Who has:
©2012, TESCCC
Hexagon
Polygon with
 8 sides
 8 angles
 8 vertices
Octagon
Figure made by two rays
that share an endpoint
that is the same shape as
the corner of a square,
90 
Right angle
Angle with a measure
less than 90 
09/19/12
page 5 of 7
Grade 6
Mathematics
Unit: 06 Lesson: 02
I Have, Who Has?
I have:
Who has:
I have:
Who has:
I have:
Who has:
©2012, TESCCC
Acute angle
Angle whose measure is
greater than 90  , but less
than 180º
Obtuse angle
Same size, same shape,
same length, or same
measure
Congruent
Set of all points that are the
same distance from its center
and lie in the same plane
09/19/12
page 6 of 7
Grade 6
Mathematics
Unit: 06 Lesson: 02
I Have, Who Has?
I have:
Circle
Who has:
Two lines in the same plane
which never intersect, and
are the same distance apart
at all points
©2012, TESCCC
09/19/12
page 7 of 7
Grade 6
Mathematics
Unit: 06 Lesson: 01
Polygon Angle Evaluation KEY
1)
 ABC shown below is an isosceles triangle.
B
A
C
a) If the measure of B is 50, what is the measure of C? Write a statement to verify your
response.
65
The sum of the angles in a triangle is 180 degrees. B is the vertex angle of an isosceles
triangle. In an isosceles triangle the angles opposite congruent sides are congruent.
Therefore, the two remaining angles are congruent. 180° ─ 50° = 130°; 130° ÷ 2 = 65°
b) Measure angle C to verify your response to part a.
2)
 ABC shown below. What is the length of segment AB? Explain your answer.
B
A
C
CB  AB (Segment CB and AB are congruent); therefore, they have the same measure. The length
is 4.
The table below shows the measures of angles in triangle.
Triangle
Angle 1
Angle 2
Angle 3
1
2
3
60
45
100
60
45
30
60
90
a
Sum of
Angles
180
180
b
3) What is the value of a in the table above? Explain your answer.
m  a = 50. The sum of the angles is 180; therefore, 180 ─ 100 ─ 30 = 50.
©2012, TESCCC
09/18/12
page 1 of 5
Grade 6
Mathematics
Unit: 06 Lesson: 01
Polygon Angle Evaluation KEY
4)
 RST is shown below.
T
S
R
What is the measure of  TRS to the nearest degree? 40
5) Look at the quadrilateral below.
Classify each angle as obtuse, acute, right, or straight.
A – right
B – acute
C – obtuse
D – right
©2012, TESCCC
09/18/12
page 2 of 5
Grade 6
Mathematics
Unit: 06 Lesson: 01
Polygon Angle Evaluation KEY
6) Look at the parallelogram ABCD shown below.
Estimate the measure of each angle.
mABC - 135
mBCD - 45
mCDA - 135
mDAB - 45
7) Look at the parallelogram RSTU shown below.
Circle whether the estimate is reasonable or not reasonable.
STU  45
Reasonable
Not Reasonable
RUT  45
Reasonable
Not Reasonable
RST  135
Reasonable
Not Reasonable
TSR  45
Reasonable
Not Reasonable
©2012, TESCCC
09/18/12
page 3 of 5
Grade 6
Mathematics
Unit: 06 Lesson: 01
Polygon Angle Evaluation KEY
8) Look at the figure below:
75
a) Name all of the acute angles in the figure.
A, D, and F
b) Name all of the obtuse angles in the figure.
B and C
9) Erika’s yard is shaped like an isosceles trapezoid. Find the measure of C to the nearest degree.
60
10) A triangle has angles measuring 45 and 50. What is the measure of the third angle?
85
©2012, TESCCC
09/18/12
page 4 of 5
Grade 6
Mathematics
Unit: 06 Lesson: 01
Polygon Angle Evaluation KEY
11) Cathy’s pool is in the shape of a trapezoid. What is the measure of F? Explain your answer.
140. The sum of the angles of a quadrilateral is 360. 360 ─ 100 ─ 80 ─ 40 = 140
12) The angle at each vertex of a regular hexagon is 120. What type of angle is at each vertex on a
regular hexagon? Why?
Obtuse, they are all congruent; therefore, they are all 120.
13) A parallelogram is shown below. Find the measure of A to the nearest degree. Explain your
answer.
A
60. Opposite angles of a parallelogram are equal.
©2012, TESCCC
09/18/12
page 5 of 5
Grade 6
Mathematics
Unit: 06 Lesson: 01
Polygon Angle Evaluation
1)
 ABC shown below is an isosceles triangle.
B
A
C
a) If the measure of B is 50, what is the measure of C? Write a statement to verify your
response.
b) Measure angle C to verify your response to part a.
2)
 ABC shown below. What is the length of segment AB? Explain your answer.
B
A
C
The table below shows the measures of angles in triangle.
Triangle
Angle 1
Angle 2
Angle 3
1
2
3
60
45
100
60
45
30
60
90
a
Sum of
Angles
180
180
b
3) What is the value of a in the table above? Explain your answer.
©2012, TESCCC
09/19/12
page 1 of 5
Grade 6
Mathematics
Unit: 06 Lesson: 01
Polygon Angle Evaluation
4)
 RST is shown below.
T
S
R
What is the measure of  TRS to the nearest degree?
5) Look at the quadrilateral below.
Classify each angle as obtuse, acute, right, or straight.
A
B
C
D
©2012, TESCCC
09/19/12
page 2 of 5
Grade 6
Mathematics
Unit: 06 Lesson: 01
Polygon Angle Evaluation
6) Look at the parallelogram ABCD shown below.
Estimate the measure of each angle.
mABC mBCD mCDA mDAB -
7) Look at the parallelogram RSTU shown below.
Circle whether the estimate is reasonable or not reasonable.
STU  45
Reasonable
Not Reasonable
RUT  45
Reasonable
Not Reasonable
RST  135
Reasonable
Not Reasonable
TSR  45
Reasonable
Not Reasonable
©2012, TESCCC
09/19/12
page 3 of 5
Grade 6
Mathematics
Unit: 06 Lesson: 01
Polygon Angle Evaluation
8) Look at the figure below.
75
a) Name all of the acute angles in the figure.
b) Name all of the obtuse angles in the figure.
9) Erika’s yard is shaped like an isosceles trapezoid. Find the measure of C to the nearest degree.
10) A triangle has angles measuring 45 and 50. What is the measure of the third angle?
©2012, TESCCC
09/19/12
page 4 of 5
Grade 6
Mathematics
Unit: 06 Lesson: 01
Polygon Angle Evaluation
11) Cathy’s pool is in the shape of a trapezoid. What is the measure of F? Explain your answer.
12) The angle at each vertex of a regular hexagon is 120. What type of angle is at each vertex on a
regular hexagon? Why?
13) A parallelogram is shown below. Find the measure of A to the nearest degree. Explain your
answer.
A
©2012, TESCCC
09/19/12
page 5 of 5