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Mr. Wolf
Friday 9/12/08
Geometry
Grades 10-12
Unit 1: Points, Lines, Planes, and Angles
Angles II
Materials and Resources:
 Warm-up (1 per student)
 How to Measure with a Protractor (1 per student)
 Graph paper (1 per student)
 Measuring with a Protractor sheet (1 per student)
 Two Postulates and Special Pairs of Angles (1 per student)
 Weekly Self-Assessments (1 per student)
PA Standards Addressed:
2.3.8 C. Measure angles in degrees and determine relations of angles.
Instructional Objectives:
 Students will be able to measure angles using a protractor in order to identify
acute, obtuse, right, straight, congruent, and adjacent angles, and angle bisectors.
 Students will be able to define and apply the Protractor Postulate, Angle Addition
Postulate, and Theorem 2-3.
 Students will be able to identify and define complementary, supplementary, and
vertical angles.
Time
Activity
Description
10 min
Warm-up
Pass out the warm-up exercise and review solutions.
5 min
Homework Check
Spot-check student homework exercises.
10 min
Homework Review Provide solutions to homework and answer any
student questions.
10 min
How to Use a
Modeling: Pass out the graph paper, protractors, and
Protractor
Measuring with a Protractor sheet. Show students the
proper way to use a protractor with the help of the
SmartBoard file.
10 min
Measuring with a
Guiding: Help students complete the activity.
Protractor
Independent Practice: Measuring Angles Activity
Activity
Assessment: Review solutions.
Modifications:
Students with special needs will be given pre-drawn
figures to measure.
Advanced students will be asked to draw their figures
on the board or overhead.
5 min
Two Postulates and Modeling: Present the two angle postulates.
Special Pairs of
Guiding: Help students complete the activity.
Angles sheet
Independent Practice: Measuring Angles Activity 1.
Assessment: Review solutions.
10 min
Measuring with a
Modifications:
Protractor
Students with special needs will be given pre-drawn
Activity #1
figures to measure.
10 min
Two Postulates and
Special Pairs of
Angles sheet
10 min
Measuring with a
Protractor
Activity #2
10 min
Measuring with a
Protractor Activity
#3
10 min
Conclusion
Homework:
None – weekend!
Lesson Reflection:
Advanced students will be asked to draw their figures
on the board or overhead.
Modeling: Present the three definitions
(supplementary, complementary, and vertical angles).
Guiding: Help students complete the activity.
Independent Practice: Measuring Angles Activity 2.
Assessment: Review solutions.
Modifications:
Students with special needs will be given pre-drawn
figures to measure.
Advanced students will be asked to draw their figures
on the board or overhead.
Modeling: Provided during lesson.
Guiding: Help students complete the activity.
Independent Practice: Measuring Angles Activity 2.
Assessment: Review solutions.
Modifications:
Students with special needs will be given pre-drawn
figures to measure.
Advanced students will be asked to draw their figures
on the board or overhead.
Weekly Self-Assessments
Geometry Fall 2008
Name: ________________________
Warm-up
1) What three figures make up an angle?
2) What is the name of an angle whose measure is between 1°-89°?
3) How many degrees are in a right angle?
4) How many degrees are in a straight angle?
5) What does an angle bisector do to an angle?
6) What makes two angles congruent?
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Geometry Fall 2008
Name: ________________________
Warm-up
1) What three figures make up an angle?
2) What is the name of an angle whose measure is between 1°-89°?
3) How many degrees are in a right angle?
4) How many degrees are in a straight angle?
5) What does an angle bisector do to an angle?
6) What makes two angles congruent?
Geometry Fall 2008
Name: ________________________
How to Measure with a Protractor
Step 1:
Identify the angle (two rays and shared vertex) that you would like to measure.
Step 2:
Place the straight edge of the protractor along one of the rays so that the vertex of the
angle is directly in the middle of this edge (there is a hole in the protractor that the vertex
should line up with)
Step 3:
The measure of the angle is the number on the protractor where that the other ray lands
upon (extend the line to reach the edge of the protractor if necessary)
Be careful!
If the angle is acute, use the smaller number (between 0°-90°).
If the angle is obtuse, use the larger number (between 90°-180°)
Examples:
Geometry Fall 2008
Name: ________________________
Measuring with a Protractor
Activity #1:
Protractor Postulate
1) Find the location of ray BD and ray BE on a protractor by lining the straight edge
with the line AC with the protractor hole over vertex B.
2) Use the Protractor Postulate to find mDBE .
Angle Addition Postulate
1) Using a protractor, find mMON and mNOP .
mMON = _________
mNOP = _________
2) Apply the Angle Addition Postulate and calculate mMOP .
3) Confirm your answer by measuring MOP with a protractor.
mMOP =_________
Activity #2:
Special Pairs of Angles
1) Using a protractor, find mKLI and mGHJ
mKLI = _________
mGHJ = _________
2) Are these angles complementary, supplementary, or vertical?
3) How do you know?
Special Pairs of Angles
1) Using a protractor, find mABC and mEFD
mABC = _________
mEFD = _________
2) Are these angles complementary, supplementary, or vertical?
3) How do you know?
Special Pairs of Angles
1) Using a protractor, measure angles 1, 2, 3, and 4
m1= _________
m2 = _________
m3 = _________
2) What kind of angles are 1 and 3? 2 and 4?
3) How do you know?
m4 = _________
Activity #3:
Angles in Shapes
1) Using a protractor, find the following angle measures:
mTUV = _________
mUTV = _________
mTVU = _________
2) Add the three angle measures together. What do you get? __________
Angles in Shapes
1) Using a protractor, find the following angle measures:
mABD = _________
mACD = _________
mCDB = _________
mBAC = _________
2) Add the four angle measures together. What do you get? __________
3) Do you notice anything between this total angle measure and the total angle
measure you found for triangle TUV?
Geometry Fall 2008
Name: ________________________
Two Postulates and Special Pairs of Angles
Protractor Postulate:
m ABC  x  y
Angle Addition Postulate:
IF point B lies in the interior of AOC
THEN mAOB  mBOC  mAOC .
IF AOC is a straight angle and B is any point not on AC
THEN mAOB  mBOC  180
complementary angles -
supplementary angles -
vertical angles -
Weekly Self-Assessment
Name: _______________________
Class: __________
Date: __________
Directions: Please fill out the following prompts and describe your learning experiences
during this week’s class. Be honest! These sheets are not graded and are used to refine
and improve lessons for the future.
1. This week I have learned…
2. This week I successfully…
3. But I had difficulty with…
4. My favorite part(s) of this week….
------------------------------DO NOT WRITE BELOW THIS LINE-----------------------------Teacher Comments/Evaluation: