Download Geometry Week 2 Packet Page 1

Geometry
Level 2
Ms. Sheppard-Brick
Do Now 4
Name:
Date:
Do Now 4 – Points, Lines, and Planes
Directions: Use the figure at the right to decide whether the statement is true or false.
1. C lies on line d.
2. X, Y, and Z are collinear.
3. A is a plane.
4. 𝐶𝑌 is a line.
Directions: Use the figure at right to answer the following questions.
5. Name the points on plane S.
6. Name two lines.
7. Name the plane that contains point D.
8. Name three collinear points.
9. Decide whether the following statement is true or false: Points K, F, and F are coplanar.
Geometry Week 2 Packet Page 1
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Intersections – Notes
Name:
Date:
Intersections – Guided Notes and Investigation
Investigation
Group Roles
List the names of the person in your group who is filling each group role.
Facilitator ___________________
Reader __________________________
Materials Manager __________________
Recorder ______________________
Materials:
•
•
•
2 pencils
3 index cards
1 pair of scissors
Instructions
The pencils will represent lines and the index cards will represent planes. Because planes are
flat, you should not bend or fold the index cards when you are using them as a model. You may
want to cut them though.
1. Model the intersection of two lines with your pencils. Determine whether two lines can
meet: one time, two times, an infinite number of times. Draw a sketch of any
intersections that are possible.
Can two lines intersect once?
Can two lines intersect exactly
twice?
Can two lines intersect an
infinite number of times?
Yes or No (circle one)
Yes or No (circle one)
Yes or No (circle one)
If yes, sketch the intersection.
If yes, sketch the intersection.
If yes, sketch the intersection.
Geometry Week 2 Packet Page 2
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Intersections – Notes
Name:
Date:
2. Model the intersection of two planes using the index cards. Determine whether two
planes can intersect: one time, two times, and infinite number of times. (Hint, cut your
index cards as shown below to make them intersect.)
Intersecting Planes with Index Cards: Cut each index card where the dotted line is. F it one index card into the other. Can two planes intersect once?
Can two planes intersect
exactly twice?
Can two planes intersect an
infinite number of times?
Yes or No (circle one)
Yes or No (circle one)
Yes or No (circle one)
If yes, sketch the intersection.
If yes, sketch the intersection.
If yes, sketch the intersection.
3. Model the intersection of a line and a plane using one pencil and one index card.
Determine whether a line and a plane can intersect: one time, two times, and infinite
number of times. You may need to poke a hole in your plane to find some intersections.
Can a line and a plane intersect
once?
Can a line and a plane
intersect exactly twice?
Can a line and a plane
intersect an infinite number of
times?
Yes or No (circle one)
Yes or No (circle one)
Yes or No (circle one)
If yes, sketch the intersection.
If yes, sketch the intersection.
If yes, sketch the intersection.
Geometry Week 2 Packet Page 3
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Intersections – Notes
Name:
Date:
Formalize
If two lines intersect once, they intersect at a _________________.
If two lines intersect an infinite number of times, they intersect at a ______________.
If two planes intersect once, they intersect at a ________________.
If two planes intersect an infinite number of times, they intersect at a ___________.
If a line and a plane intersect once, they intersect at a ________________.
If a line and a plane intersect an infinite number of times, they intersect at a ___________.
Practice
Geometry Week 2 Packet Page 4
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Intersections – Notes
Name:
Date:
Directions: Sketch the figure described.
8. Sketch a plane and a line that intersects the plane. Then sketch a line in the plane that intersects
the first line.
9. Sketch a plane and a line that intersects the plane. Then sketch another line that intersects the
plane and does not intersect the first line.
10. Sketch two planes that intersect in a line. Then sketch a line that intersects each of the planes, but
does not intersect the first line.
Geometry Week 2 Packet Page 5
Geometry Level 2
Homework 5
Name:
Date:
Homework 5 – Sketching Intersections
Directions: For each of the following problems, name the intersection, or write ‘no intersection.’
1) The intersection of
.
2) The intersection of
.
3) The intersection of
.
4) The intersection of Y and Z.
5) The intersection of W and Y.
6) The intersection of X and Z.
Directions: Sketch each of the figures described.
7) Three lines that lie in a plane and intersect in a point
8) Three planes that do not intersect
9) Two lines in a plane that do not intersect
10) A line that intersects a plane at a point
Directions: for problem 11, show your work and/or explain how you got your answer for each
part of the problem.
11) Briana is finding real world examples for geometric intersections. She thinks that two
railroad tracks might represent lines and the switch (where they meet) would represent the
point of intersection.
a) Give another real world example of two lines and their intersection. Be sure to explain what
represent the lines and what represents the intersection.
b) Give a real world example of figures that represent two planes and their intersection. Be sure
to explain what represent the planes and what represents the intersection.
c) Give a real world example of figures that represent two coplanar lines that do not intersect. Be
sure to example what represents the plane and what represents the lines.
Geometry Week 2 Packet Page 6
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Do Now 5
Name:
Date:
Do Now 5 – Solving Equations Practice
Directions: Solve the following equations for the variable. Show your work.
1. 5x – 3 = 2
2. 3n + 2 = 17
Geometry Week 2 Packet Page 7
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Segments & Measures
Name:
Date:
Segments and Their Measures – Guided Notes Vocabulary Coordinate – the real number that corresponds to a ______________________. Distance (aka length of a segment) Definition: Notation Figure Example(s): Example 1: measure the length of each segment in centimeters. Round to the nearest tenth. a. b. Between – Definition: Notation Figure Example(s): Geometry Week 2 Packet Page 8
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Segments & Measures
Name:
Date:
Segment Addition Postulate: If point B is between points A and C, then AC = AB + BC If: Then: x
x+y
y
C
B
A
B
A
Converse of the Segment Addition Postulate: If AC = AB + AC, then point B is between points A and C. If: Then: x+y
A
x
A
C
B
C
y
B
C
Example 2: Find the length of the segment indicated. a. Find AC b. Find DE Congruent Segments – Definition: Figure Notation Example(s): Geometry Week 2 Packet Page 9
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Segments & Measures
Name:
Date:
Example 3: Determine whether the segments are congruent. Example 4: Draw a sketch of the three collinear points. Then write the Segment Addition Postulate for the points. a. E is between D and F b. H is between G and J c. M is between N and P d. R is between Q and S Geometry Week 2 Packet Page 10
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Segments & Measures
Name:
Date:
Practice Directions: Use the diagram to determine whether the statement is true or false. 1. B is between A and C. C
2. E is between C and F. B
3. E is between D and H. 4. D is between A and H. E
A
D
5. C is between B and E. Directions: Find the length of the given segment. 6. Find PR 7. Find SU P
Q
9 cm
R
7 cm
8. Find MN S
5 cm
T
H
F
16 cm
9. Find JK G
U
21 cm
L
M
11 cm
23 cm
N
J
K
17 cm
L
Directions: Determine which segments in the coordinate plane are congruent. 10. 4
A
2
C
D
–5
5
F
–2
B
E
G
–4
–6
H
Geometry Week 2 Packet Page 11
Homework 6
Name:
Date:
Geometry Level 2
Homework 6 – Segments and Their Measures
Directions: Use a ruler to find the length of each segment. Measure in centimeters and round to
the nearest tenth of a cm.
Directions: Use the segment addition postulate to find the length of each segment. All
measurements are in centimeters.
5.
6.
7.
8.
Directions: Write an algebraic expression for the length of each segment.
9. Write an expression for EG (the length of
segment EG.)
10. Write an expression for LM (the length of
segment LM.)
Directions: for problem 11, show your work and/or explain how you got your answer for each
part of the problem.
11. The rectangle shown below is a scale model of Elizabeth’s room where 1 cm = 1 m (1
centimeter on the diagram is equal to 1 meter in the room.)
a. Find the length of AB to the nearest tenth of a centimeter.
b. What is the length of Elizabeth’s bedroom (represented by AB?)
A
B
D
C
c. Find the length of AD to the nearest tenth of a centimeter.
d. What is the width of Elizabeth’s bedroom (represented by AD?)
e. What is the area of Elizabeth’s bedroom in square meters?
Geometry Week 2 Packet Page 12
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Vocabulary Angle – Definition: Figure Angles & Measures
Name:
Date:
Angles and Their Measures – Guided Notes and Practice Sides of an Angle – Definition: Figure Vertex of an Angle – Definition: Figure Measure of an Angle – Notation Example(s): Notation Example(s): Notation Example(s): Geometry Week 2 Packet Page 13
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Definition: Figure Angles & Measures
Name:
Date:
Notation Example(s): Measuring an Angle 1. Place the center of the protractor over the vertex of the angle. 2. Align the protractor with one side of the angle. 3. Read where the second side of the angle crosses the protractor. Example 1: Name each angle and measure each angle to the nearest degree. a. b. A
E
B
C
c. F
D
d. I
L
H
G
Classifying Angles K
J
Geometry Week 2 Packet Page 14
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Angles & Measures
Name:
Date:
Angles with a measure between 0° and 90°. Angles with a measure between 90° and 180°. Angles with a measure of 90°. Angles with a measure of 180°. Example 2: Classify each angle. a. m∠𝐴 = 130° b. m∠𝐵 = 90° c. m∠𝐶 = 45° Angle Addition Postulate If P is in the interior of ∠𝑅𝑆𝑇, then the measure of ∠𝑅𝑆𝑇 is the sum of the measures of ∠𝑅𝑆𝑃 𝑎𝑛𝑑 ∠𝑃𝑆𝑇. If: Then: R
R
(x + y)°
x°
S
P
P
y°
S
T
Example 3: Find the measure of ABC. a. b. T
Geometry
Week 2 Packet Page 15
c. Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
A
A
40°
A
D
40°
Angles & Measures
Name:
Date:
C
D
60°
90°
20°
B
B
90°
C
C
B
D
Practice Directions: Name the vertex and sides of each angle. Then name the angle in two ways 1. 2. 3. T
S
R
F
X
O
K
N
E
Vertex: Vertex: Vertex: Sides: Sides: Sides: Angle Names: Angle Names: Angle Names: Directions: Measure each angle to the nearest degree, then classify the angle. 4. 5. 6. T
S
R
F
X
O
Measure: Measure: Classify: Classify: Directions: Find the measure of the angle. 7. m∠𝐷𝐸𝐹 = 8. m∠𝐺𝐸𝐹 = K
N
E
Measure: Classify: 9. m∠DEF = Geometry Week 2 Packet Page 16
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Angles & Measures
Name:
Date:
D
G
G
45°
D
F
D
60°
60°
E
G
95°
E
F
160°
60°
E
F
Directions: Plot the points on the coordinate plane. Then measure angle ABC and classify it. 10. A (3, 0), B (0, 0), and C (0, 3) 11. A (3, 0), B (0, 0), and C (4, -­‐4) 4
4
2
2
–5
5
–5
5
–2
–2
–4
Measure: Classification: 12. A (-­‐3, 0), B (0, 0), and C (2, -­‐2) –4
4
4
2
2
–5
5
–5
5
–2
–4
Measure: Classification: Measure: Classification: 13. A (0, 4), B (0, 0), and C (2, 2) –2
–4
Measure: Classification: Geometry Week 2 Packet Page 17
Geometry Level 2
Homework 7
Name:
Date:
Homework 7 – Angles and Their Measures
Directions: Use a protractor to measure the angle to the nearest degree. Then state whether the
angle is acute, obtuse, right, or straight.
1.
2.
3.
Directions: Find the measure of the indicated angle.
4. Find m∠JKN
5. Find m∠𝐸𝐹𝐻
6. Find m∠𝑅𝑄𝑡
7. Find m∠𝑅𝐸𝑍
8. Find m∠𝑅𝑇𝑆
9. Find m∠GPS
Directions: for problem 10, show your work and/or explain how you got your answer for each
part of the problem.
B
10. Anthony sketched the figure at right and measured some of the angles.
a. Find the measure of ∠𝐹𝐺𝐸. Show or explain how you got your answer.
62°
A
c. Find the measure of ∠𝐴𝐺𝐵. Show or explain how you got your answer.
54°
G
b. Find the measure of ∠𝐴𝐺𝐹. Show or explain how you got your answer.
F
Geometry Week 2 Packet Page 18
C
D
E