name 1 points, lines & planes hw section...
TRANSCRIPT
![Page 1: Name 1 Points, Lines & Planes Hw Section 1smacmathgeometry.weebly.com/.../5/19254419/g_hw_q1.pdf · Segments, Distance & Midpoint Hw Section 1.2 Use the picture for questions 1 –](https://reader030.vdocuments.net/reader030/viewer/2022040104/5e9efb2d58742e6727392b19/html5/thumbnails/1.jpg)
Name _________________ 1
Geometry 1
Points, Lines & Planes Hw Section 1.1
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Geometry 2
Geometry 2
![Page 3: Name 1 Points, Lines & Planes Hw Section 1smacmathgeometry.weebly.com/.../5/19254419/g_hw_q1.pdf · Segments, Distance & Midpoint Hw Section 1.2 Use the picture for questions 1 –](https://reader030.vdocuments.net/reader030/viewer/2022040104/5e9efb2d58742e6727392b19/html5/thumbnails/3.jpg)
Name _________________ 3
Geometry 3
Points, Lines & Planes Application Section 1.1
Watch the application walk through video if you need extra help getting started on Flippedmath.com
![Page 4: Name 1 Points, Lines & Planes Hw Section 1smacmathgeometry.weebly.com/.../5/19254419/g_hw_q1.pdf · Segments, Distance & Midpoint Hw Section 1.2 Use the picture for questions 1 –](https://reader030.vdocuments.net/reader030/viewer/2022040104/5e9efb2d58742e6727392b19/html5/thumbnails/4.jpg)
Geometry 4
Geometry 4
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Name _________________ 5
Geometry 5
Segments, Distance & Midpoint Hw Section 1.2 Use the picture for questions 1 – 4.
1. Find AB 2. Find EC
3. What is the midpoint of 𝐶𝐸̅̅ ̅̅ ?
4. Is 𝐵𝐷̅̅ ̅̅ ≅ 𝐶𝐴̅̅ ̅̅ ? Explain why or why not. Label the picture, then find the length of the given segment.
Find BI
Find FU
Find EA
11. If AD = 12 and AC = 4y – 36, find the value of y. Then find DC.
12. If ED = x + 4 and DB 3x – 8, find ED and DB.
Draw and label a picture for each of the following. Indicate what line segments are congruent (if any). 13. A is the midpoint of 𝐻𝑇̅̅ ̅̅
14. 𝐷𝑄̅̅ ̅̅ bisects 𝑅𝐹̅̅ ̅̅ at M.
15. 𝑇𝑀⃗⃗⃗⃗ ⃗⃗ bisects 𝑊𝐸̅̅ ̅̅ ̅ at T
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Geometry 6
Geometry 6
Find the midpoint and distance given the two endpoints 16. (12,15) and (-8, -22) 17. (-3,5) and (14, 28)
Find the midpoint and distance given the two endpoints 18.
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Name _________________ 7
Geometry 7
Segments, Distance & Midpoint Application Section 1.2
Watch the application walk through video if you need extra help getting started on Flippedmath.com
![Page 8: Name 1 Points, Lines & Planes Hw Section 1smacmathgeometry.weebly.com/.../5/19254419/g_hw_q1.pdf · Segments, Distance & Midpoint Hw Section 1.2 Use the picture for questions 1 –](https://reader030.vdocuments.net/reader030/viewer/2022040104/5e9efb2d58742e6727392b19/html5/thumbnails/8.jpg)
Geometry 8
Geometry 8
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Name _________________ 9
Geometry 9
End of Course Test Questions The key to this section is on smacmathgeometry.weebly.com under “Air Test”
2017
Question 2
Line segment AB has endpoints 𝐴(−1.5, 0) and 𝐵(4.5, 8). Point C is on line segment AB and is located at (0, 2). What is the
ratio of 𝐴𝐶
𝐶𝐵?
2017
![Page 10: Name 1 Points, Lines & Planes Hw Section 1smacmathgeometry.weebly.com/.../5/19254419/g_hw_q1.pdf · Segments, Distance & Midpoint Hw Section 1.2 Use the picture for questions 1 –](https://reader030.vdocuments.net/reader030/viewer/2022040104/5e9efb2d58742e6727392b19/html5/thumbnails/10.jpg)
Geometry 10
Geometry 10
2018
2019
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Name _________________ 11
Geometry 11
Angles Measures Hw Section 1.3
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Geometry 12
Geometry 12
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Name _________________ 13
Geometry 13
Angles Measures Application Section 1.3
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Geometry 14
Geometry 14
?
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Name _________________ 15
Geometry 15
Addition Postulates Hw Section 1.4
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Geometry 16
Geometry 16
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Name _________________ 17
Geometry 17
Addition Postulates Application Section 1.4
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Geometry 18
Geometry 18
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Name _________________ 19
Geometry 19
Angle Pairs Hw Section 1.5
1. Solve the following. a) x = ________ y = ________
b) x = ________ y = ________
c) x = ________ y = ________
Use the figure below to determine if each statement is true or false.
2. 5 and 3 are vertical angles. T or F
3. 1 and 5 are a linear pair. T or F
4. 4 and 3 are adjacent angles. T or F
5. 4 and 1 are vertical angles. T or F
6. 3 and 4 are a linear pair. T or F
7. If 1 and 2 are supplements and m1 = 150, what is
m2? ___________
8. If 1 and 2 are complements and m1 = 27, what is
m2? ___________
9. If 1 and 2 are vertical angles and m1 = 36, what is
m2? ___________
10. If 1 and 2 are a linear pair and m1 = 2x + 8 and
m2 = 3x + 2, what is the value of x? x = _______
11. If 1 and 2 are vertical angles and m1 = 7x – 5 and
m2 = 4x + 10, what is the value of x? x = _______
yx
67°
y
3x - 5
127°
y5x - 15
54
32
1
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Geometry 20
Geometry 20
12. Find the value of x.
13. Find the value of x.
14. Find the value of x.
15. The m∠ABD = 5x – 11, m∠CBD = 4x + 38. Find m∠ABD. 16. m∠FOM = 2x + 13, m∠MOX = 3x – 3 and ∠FOX is a right angle. Find the value of x. 17. ∠BOT is a right angle, m∠DOG = 2x – 4, m∠HOT = x + 16. Find m∠DOC.
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Name _________________ 21
Geometry 21
Angle Pairs Application Section 1.5
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Geometry 22
Geometry 22
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Name _________________ 23
Geometry 23
Tools for Geometry Review Chapter 1
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Geometry 24
Geometry 24
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Name _________________ 25
Geometry 25
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Geometry 26
Geometry 26
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Name _________________ 27
Geometry 27
Inductive Reasoning Hw Section 2.1
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Geometry 28
Geometry 28
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Name _________________ 29
Geometry 29
Inductive Reasoning Application Section 2.1 If the given statement is not in if-then form, write it in if-then form. Identify the hypothesis and the conclusion. Then write the contrapositive. Determine the true-value of both statements.
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Geometry 30
Geometry 30
End of Course Test Questions 2018 The key to this section is on smacmathgeometry.weebly.com under “Air Test”
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Name _________________ 31
Geometry 31
Algebraic Proofs Hw Section 2.2
𝐺𝐻 = 𝐺𝐻
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Geometry 32
Geometry 32
Proof #5.
Proof #6. Prove that if 8
3𝑥 +
1
3=
11
3𝑥 −
2
3, then x = 1.
Given:
Prove:
Statement Reason
a. a. b. b. c. c. d. d.
e. e. f. f.
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Name _________________ 33
Geometry 33
Proving Segments Hw Section 2.3 1. Prove the Midpoint Theorem using a two-column proof. Given Prove
Statement Reason
a. a. b. b. c. c. d. d.
e. e. f. f.
2. Given 𝐿𝐸̅̅̅̅ ≅ 𝑀𝑅̅̅ ̅̅̅, 𝐸𝐺̅̅ ̅̅ ≅ 𝑅𝐴̅̅ ̅̅
Prove 𝐿𝐺̅̅̅̅ ≅ 𝑀𝐴̅̅ ̅̅̅
Statement Reason
a. a. Given b. 𝐿𝐸 = 𝑀𝑅 b. 𝐸𝐺 = 𝑅𝐴
c. 𝐿𝐺 = 𝐿𝐸 + 𝐸𝐺 c. 𝑀𝐴 = 𝑀𝑅 + 𝑅𝐴 d. 𝐿𝐺 = 𝑀𝑅 + 𝑅𝐴 d. Substitution Property of Equality (double)
e. e. Substitution Property of Equality
f. 𝐿𝐺̅̅̅̅ ≅ 𝑀𝐴̅̅ ̅̅̅ f.
L
•
G
•
M
•
A
•
R
•
E
•
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Geometry 34
Geometry 34
3. Given 𝐷𝐴 = 𝐸𝐿 Prove 𝐷𝐸 = 𝐴𝐿
Statement Reason
a. a. Given b. 𝐷𝐴 = 𝐷𝐸 + 𝐸𝐴 b. 𝐸𝐿 = 𝐸𝐴 + 𝐴𝐿
c. c. Substitution Property of Equality d. 𝐷𝐸 = 𝐴𝐿 d.
4. Given 𝑅𝑆 = 𝑆𝑇 Prove 𝑅𝑇 = 2𝑆𝑇
Statement Reason
a. a. b. b. c. c. d. d.
e. e. f. f.
E
•
L
•
D
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A
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T
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R
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Name _________________ 35
Geometry 35
Proving Segments Application Section 2.3
1. Given 𝑆𝐴̅̅̅̅ ≅ 𝑁𝐷̅̅ ̅̅
Prove 𝑆𝑁̅̅ ̅̅ ≅ 𝐴𝐷̅̅ ̅̅
Statement Reason
a. a. b. b. c. c. d. d.
e. e. f. f.
2. Given 𝑀𝑃 = 𝑁𝑃
𝑃𝑂 = 𝑃𝐿 Prove 𝑀𝑂 = 𝑁𝐿
Statement Reason
a. a. b. b. c. c. d. d.
e. e. f. f.
A
•
D
•
S
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N
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P
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M
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• N
• O
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Geometry 36
Geometry 36
3. Given 𝐴𝐶 = 𝐴𝐷
𝐴𝐵 = 𝐴𝐸 Prove 𝐵𝐶 = 𝐸𝐷
Statement Reason
a. a. b. b. c. c. d. d.
e. e. f. f.
A
•
• E
• D
B •
C •
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Name _________________ 37
Geometry 37
Proving Angles Hw Section 2.4 1.
Given ∠1 and ∠2 form a linear pair ∠2 and ∠3 form a linear pair
Prove ∠1 ≅ ∠3
Statement Reason
a. a. b. b. c. c. d. d.
e. e. f. f.
2.
Given 𝑚∠𝑅𝑆𝑊 = 𝑚∠𝑇𝑆𝑈
Prove 𝑚∠𝑅𝑆𝑇 = 𝑚∠𝑊𝑆𝑈
Statement Reason
a. a.
b. b. c. c. d. d.
e. e. f. f.
1
3
4 2
S R
W
T
U
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Geometry 38
Geometry 38
3.
Given ∠1 ≅ ∠3
Prove ∠2 ≅ ∠4
Statement Reason
a. a. b. b. c. c. d. d.
e. e. f. f.
g. g. h. h. i. i.
2 1
5
4 3
6
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Name _________________ 39
Geometry 39
Proving Angles Application Section 2.4 1.
Given ∠𝑄𝑃𝑆 ≅ ∠𝑇𝑃𝑅
Prove ∠𝑄𝑃𝑅 ≅ ∠𝑇𝑃𝑆
Statement Reason
a. a. b. 𝑚∠𝑄𝑃𝑆 = 𝑚∠𝑇𝑃𝑅 b. c. 𝑚∠𝑄𝑃𝑆 = 𝑚∠𝑄𝑃𝑅 + 𝑚∠𝑅𝑃𝑆 c. 𝑚∠𝑇𝑃𝑅 = 𝑚∠𝑇𝑃𝑆 + 𝑚∠𝑅𝑃𝑆 d. d. Substitution Property of Equality
e. e. f. f.
P Q
S R T
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Geometry 40
Geometry 40
2. Given ∠1 and ∠2 form a linear pair
∠2 and ∠3 are supplementary
Prove ∠1 ≅ ∠3
Statement Reason
a. a. b. b. c. c. d. d.
e. e. f. f.
g. g. h. h.
2 1
3
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Name _________________ 41
Geometry 41
Reasoning & Proof Review Chapter 2
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Geometry 42
Geometry 42
14.
15.
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Name _________________ 43
Geometry 43
16. Given M is the midpoint of 𝐴𝐵̅̅ ̅̅ B is the midpoint of 𝑀𝐷̅̅ ̅̅ ̅ Prove MD = 2MB
Statements Reasons
a. M is the midpoint of 𝐴𝐵̅̅ ̅̅ a. B is the midpoint of 𝑀𝐷̅̅ ̅̅ ̅ b. AM = MB b. MB = BD c. MD = MB + BD c. d. MD = MB + MB d. e. MD = 2MB e.
17. Given M is the midpoint of 𝑆𝑇̅̅̅̅ Prove ST = 2MT
Statements Reasons
a. a.
b. b.
c. c.
d. d.
e. e.
f. f.
g. g.
S M T
• A
• M
• D
• B
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Geometry 44
Geometry 44
18.
Given ∠𝑄𝑃𝑆 ≅ ∠𝑇𝑃𝑅
Prove ∠𝑄𝑃𝑅 ≅ ∠𝑇𝑃𝑆
Statement Reason
a. a. b. 𝑚∠𝑄𝑃𝑆 = 𝑚∠𝑇𝑃𝑅 b. c. 𝑚∠𝑄𝑃𝑆 = 𝑚∠𝑄𝑃𝑅 + 𝑚∠𝑅𝑃𝑆 c. 𝑚∠𝑇𝑃𝑅 = 𝑚∠𝑇𝑃𝑆 + 𝑚∠𝑅𝑃𝑆 d. d. Substitution Property of Equality
e. e. f. f.
P Q
S
R
T
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Name _________________ 45
Geometry 45
Lines & Angles Hw Section 3.1
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Geometry 46
Geometry 46
End of Course Test Questions 2017 The key to this section is on smacmathgeometry.weebly.com under “Air Test”
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Name _________________ 47
Geometry 47
Properties of Parallel Lines Hw Section 3.2 Directions: Identify all the numbered angles that are congruent to the given angle. JUSTIFY your answer.
Directions: Solve for x.
Directions: Find the measure of the angle indicated in bold.
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Geometry 48
Geometry 48
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Name _________________ 49
Geometry 49
End of Course Test Questions 2018
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Geometry 50
Geometry 50
End of Course Test Questions 2019
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Name _________________ 51
Geometry 51
Proving Lines Parallel Hw Section 3.3
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Geometry 52
Geometry 52
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Name _________________ 53
Geometry 53
Parallel Lines and Triangles Hw Section 3.4
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Geometry 54
Geometry 54
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Name _________________ 55
Geometry 55
Equations of Lines in the Coordinate Plane Hw Section 3.5
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Geometry 56
Geometry 56
Directions: Write the equation of a line with the given information.
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Name _________________ 57
Geometry 57
Slopes of Parallel and Perpendicular Lines Hw Section 3.6 Directions: Write the equation of the line described.
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Geometry 58
Geometry 58
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Name _________________ 59
Geometry 59
End of Course Test Questions 2017 The key to this section is on smacmathgeometry.weebly.com under “Air Test”
End of Course Test Questions 2018
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Geometry 60
Geometry 60
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Name _________________ 61
Geometry 61
Transversals Chapter 3 Review 1
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Geometry 62
Geometry 62
Write the equation of a line from the given information.
![Page 63: Name 1 Points, Lines & Planes Hw Section 1smacmathgeometry.weebly.com/.../5/19254419/g_hw_q1.pdf · Segments, Distance & Midpoint Hw Section 1.2 Use the picture for questions 1 –](https://reader030.vdocuments.net/reader030/viewer/2022040104/5e9efb2d58742e6727392b19/html5/thumbnails/63.jpg)
Name _________________ 63
Geometry 63
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Geometry 64
Geometry 64
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Name _________________ 65
Geometry 65
Transversals Chapter 3 Review 2
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Geometry 66
Geometry 66
Write the equation of a line with the given information.
![Page 67: Name 1 Points, Lines & Planes Hw Section 1smacmathgeometry.weebly.com/.../5/19254419/g_hw_q1.pdf · Segments, Distance & Midpoint Hw Section 1.2 Use the picture for questions 1 –](https://reader030.vdocuments.net/reader030/viewer/2022040104/5e9efb2d58742e6727392b19/html5/thumbnails/67.jpg)
Name _________________ 67
Geometry 67
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Geometry 68
Geometry 68
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Name _________________ 69
Geometry 69
Tools, Proofs & Transversals Quarter 1 Review 1 1. Part of a proof is shown. Place statements and reasons in the table to complete the proof.
Given 𝐿𝐸̅̅̅̅ ≅ 𝑀𝑅̅̅ ̅̅̅, 𝐸𝐺̅̅ ̅̅ ≅ 𝑅𝐴̅̅ ̅̅ Prove 𝐿𝐺̅̅̅̅ ≅ 𝑀𝐴̅̅ ̅̅̅
Statement Reason
a. a. Given b. 𝐿𝐸 = 𝑀𝑅 b. 𝐸𝐺 = 𝑅𝐴
c. 𝐿𝐺 = 𝐿𝐸 + 𝐸𝐺 c. 𝑀𝐴 = 𝑀𝑅 + 𝑅𝐴 d. 𝐿𝐺 = 𝑀𝑅 + 𝑅𝐴 d. Substitution Property of Equality (double)
e. e. Substitution Property of Equality f. 𝐿𝐺̅̅̅̅ ≅ 𝑀𝐴̅̅ ̅̅̅ f.
2
3
4
𝑔
𝑐𝑚3
5
6
7
people per square mile (Round your answer to the nearest tenth.)
8
9
L
•
G
•
M
•
A
•
R
•
E
•
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Geometry 70
Geometry 70
2. Which term is defined as an angle formed by two opposite rays? A. Straight angle B. Vertical angle C. Corresponding angle D. Complementary angle
3. Kevin asked Olivia what the Supplement
Theorem is. Olivia responded, “𝑚∠1 +𝑚∠2 = 180.” What definition did Olivia actually give? A. Definition of a straight angle B. Definition of supplementary angles C. Definition of complementary angles D. Definition of transversal
4. Jeremy wants to know the density of a rock
in grams per cubic centimeter. The rock has a mass of 4.45 kilograms and a volume of 508 cubic centimeters. What is the density of the rock, in graphs per
cubic centimeter (𝑔
𝑐𝑚3)?
𝑔
𝑐𝑚3
5. Line k has a slope of 4. Line j is
perpendicular to line k and passes through the point (-2, 8). Create the equation for line j.
6. 𝐴𝐶̅̅ ̅̅ has endpoints A(-1, -3.5) and C(5, -1). Point B is on 𝐴𝐶̅̅ ̅̅ and is located at (0.2, -3).
What is the ratio of 𝐴𝐵
𝐵𝐶?
7. A study reports that in 2010 the population
of the United States was 308,745,538 people and the land area was approximately 3,531,905 square miles. Based on the study, what was the population density, in people per square mile, of the United States in 2010? Round your answer to the nearest tenth.
people per square mile
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Name _________________ 71
Geometry 71
8. Square ABCD has vertices at A(1, 2) and B(3, -3). What is the slope of 𝐵𝐶̅̅ ̅̅ ?
9. The graph of line 𝑚 is shown
What is the equation of the line that is perpendicular to line 𝑚 and passes through the point (-2, 4)?
![Page 72: Name 1 Points, Lines & Planes Hw Section 1smacmathgeometry.weebly.com/.../5/19254419/g_hw_q1.pdf · Segments, Distance & Midpoint Hw Section 1.2 Use the picture for questions 1 –](https://reader030.vdocuments.net/reader030/viewer/2022040104/5e9efb2d58742e6727392b19/html5/thumbnails/72.jpg)
Geometry 72
Geometry 72
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Name _________________ 73
Geometry 73
Tools, Proofs & Transversals Quarter 1 Review 2 1. Part of a proof is shown. Place statements and reasons in the table to complete the proof.
Given ∠1 ≅ ∠3
Prove ∠2 ≅ ∠4
Statement Reason
a. a.
b. b. c. c. d. d.
e. e. f. f.
g. g. h. h. ii. i.
2 1
5
4 3
6
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Geometry 74
Geometry 74
2
3
4
𝑔
𝑐𝑚3
5
6
7
people per square mile (Round your answer to the nearest tenth.)
8
9
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Name _________________ 75
Geometry 75
2. Which term is defined as nonadjacent angles formed by two intersecting lines? A. Straight angle B. Vertical angle C. Corresponding angle D. Complementary angle
3. Kevin asked Olivia what the Alternate
Interior Angles Theorem is. Olivia responds, “When a transversal intersects two lines, the alternate interior angles are congruent.” What is wrong with Olivia’s responds? A. She should have said the alternate
interior angles are supplementary, instead of congruent.
B. She should have said the alternate interior angles are complementary, instead of congruent.
C. She should have said the transversal intersects two parallel lines.
D. She should have said the transversal intersects two perpendicular lines.
4. Jeremy wants to know the density of a pop
tart in grams per cubic centimeter. The pop tart has a mass of 0.00183 kilograms and a volume of 97 cubic centimeters. What is the density of the pop tart, in graphs
per cubic centimeter (𝑔
𝑐𝑚3)?
𝑔
𝑐𝑚3
5. Line k has a slope of −2
3. Line j is
perpendicular to line k and passes through the point (-4, -5). Create the equation for line j.
6. 𝐴𝐶̅̅ ̅̅ has endpoints A(3, 4) and C(6, 8). Point B is on 𝐴𝐶̅̅ ̅̅ and is located at (4.5, 6). What is
the ratio of 𝐴𝐵
𝐵𝐶?
7. A study reports that in 2016 the population
of the Gnaden was 1,283 people and the land area was approximately 0.96875 square miles. Based on the study, what was the population density, in people per square mile, of the United States in 2016? Round your answer to the nearest tenth.
people per square mile
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Geometry 76
Geometry 76
8. Square ABCD has vertices at A(8, -2) and B(5, -6). What is the slope of 𝐶𝐷̅̅ ̅̅ ?
9. The graph of line 𝑚 is shown
What is the equation of the line that is perpendicular to line 𝑚 and passes through the point (4, -2)?
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Name _________________ 77
Geometry 77
Constructions – Segments & Angles Hw Section A.1 G.CO.D.12 COPYING A SEGMENT
1. Given 𝐴𝐵̅̅ ̅̅ , 𝐶𝐷̅̅ ̅̅ , & 𝐸𝐹̅̅ ̅̅ . Use the copy segment construction to create the new lengths listed below.
3AB
CD + EF
2CD + 1AB
EF - CD
CONSTRUCTING A MIDPOINT
2. Given 𝐴𝐵̅̅ ̅̅ & 𝐶𝐷̅̅ ̅̅ . Use the midpoint construction to find the midpoint of 𝐴𝐵̅̅ ̅̅ & 𝐶𝐷̅̅ ̅̅ .
3. Use your midpoint construction to determine the exact length of 1
4𝐸𝐹
A BC DE F
A B
C
D
E F
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Geometry 78
Geometry 78
4. Given ∠𝐴𝐵𝐶. Make a copy of∠𝐴𝐵𝐶, ∠𝐴′𝐵′𝐶′.
5. Given ∠𝐷𝐸𝐹. Make a copy of ∠𝐷𝐸𝐹, ∠𝐷′𝐸′𝐹′.
A
B
C
E
B'
D
E
F
E'
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Name _________________ 79
Geometry 79
PRACTICE - CONSTRUCTION BASICS #1 1. Given 𝑀𝑁̅̅ ̅̅ ̅, construct 2.5 MN
2. Given 𝐺𝐻̅̅ ̅̅ , construct 1.75 GH
3. Given ABC, construct a copy of it, A’B’C’.
M N
G H
B C
A
A
B'
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Geometry 80
Geometry 80
4. Given ABC, can you think of a way to create a line parallel to 𝐴𝐵̅̅ ̅̅ through point C? (Hint: How could copying an angle help you?)
5. Create a parallel line to 𝐷𝐸⃡⃗⃗⃗ ⃗ through point F.
BC
A
D F
E
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Name _________________ 81
Geometry 81
Perpendiculars & Bisectors Hw Section A.2 Constructing the Perpendicular Bisector (a ⊥ line through the midpoint of a segment).
1. Given 𝐴𝐵̅̅ ̅̅ . Use the midpoint construction to construct the perpendicular bisector.
Construct the perpendicular line THROUGH A POINT ON THE LINE. 2. Work backwards from the midpoint construction.
Construct the perpendicular line THROUGH A POINT not on THE LINE. 3. Work backwards through the midpoint construction.
A B
A
B
A C
B A
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Geometry 82
Geometry 82
Construct the angle bisector.
4. Given A, construct the angle bisector, 𝐴𝐷⃗⃗ ⃗⃗ ⃗
5. Given sides of a rectangle. Construct the rectangle. Hint - We need perpendicular lines through A and through B.
6. Given the side of a square. Construct the square.
A
A
A B
C
D
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Name _________________ 83
Geometry 83
End of Course Test Questions 2019
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Geometry 84
Geometry 84
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Name _________________ 85
Geometry 85
Inscribed Polygons Hw Section A.3 1. Determine whether the relationships is INSCRIBED or CIRCUMSCRIBED.
a) The triangle is _____________. b) The hexagon is _____________ c) The circle is _______________
d) The hexagon is _____________ e) The circle is _______________ f) The triangle is ______________
2. Jeff uses his compass to make a cool design. He just keeps creating congruent circles… over and over… a) Find a regular hexagon (shade it in) b) Find a different regular hexagon (shade it in)
c) Find an equilateral triangle (shade it in) d) Find a different equilateral triangle (shade it in)
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Geometry 86
Geometry 86
3. The inscribed equilateral triangle has a central angle of 120 because 360 / 3 = 120, an inscribed square has a central
angle of 90 because 360 / 4 = 90. The central angle of a decagon is 36 because 360 / 10 = 36. Use this information and a compass to create an inscribed decagon.
36°
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Name _________________ 87
Geometry 87
4. Construct the requested inscribed polygons. a) Construct an equilateral triangle inscribed in the provided circle using your compass and straightedge.
b) Construct a square inscribed in the provided circle using your compass and straightedge.
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Geometry 88
Geometry 88
5. Construct the requested inscribed polygons. a) Construct a regular hexagon inscribed in the provided circle using your compass and straightedge.
b) Construct a regular octagon inscribed in the provided circle using your compass and straightedge.
Hint: The central angle is 45, half of
the square’s central angle of 90.
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Name _________________ 89
Geometry 89
Inscribed Polygons Hw Section A.3 Part 2 Review the basic constructions.
1. Copying Segments a) 4AB – CD
b) 2.75CD + AB
2. Midpoint Construction
a) Given diameter AB, find the center
b) Which is larger AB or ½ CD? ____________
c) Construct the midpoint of 𝐴𝐵̅̅ ̅̅
d) 𝐶𝐷 =1
3𝐺𝐻. Construct 𝐺𝐻̅̅ ̅̅ .
A B C D
B
A
Copy them here to compare them
A
B
C
D
A
B
C
D
G
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Geometry 90
Geometry 90
3. Copying an Angle & Parallel Line Construction
a) Create A’B’C’ by copying ABC. b) Create D’E’F’ by copying DEF.
c) Create A’ by copying Copy A d) Create E’ such that mE’ = 2(mE)
B
A
C
B'
E
D
F
E'
A
A'
E
E'
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Name _________________ 91
Geometry 91
4. Angle Bisector Construction
a) Construct the angle bisector of A. b) Create DBC such that mDBC = ½ (mABC)
5. Perpendicular Constructions Construct the following.
a) the perpendicular bisector of 𝐴𝐷̅̅ ̅̅ b) a perpendicular line to 𝐴𝐸⃡⃗⃗⃗ ⃗ through E
c) the perpendicular line to 𝐷𝐴⃡⃗⃗⃗ ⃗ through C
A
B
A
C
A
C
E
D
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Geometry 92
Geometry 92
6. Inscribed Polygons a) Inscribed Square b) Inscribed Equilateral Triangle c) Inscribed Hexagon
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Name _________________ 93
Geometry 93
Constructions Chapter A Review
1. What is the best description for the distance from Point A to Point B?
A) 𝐴𝐵 B) 𝐴𝐵 C) about 2 cm D) about 1.5 inches
1. _____
2. What is the best description for the distance from Point A to Point B? A) CD + 2EF B) CD – EF C) 2CD – EF D) 2CD + EF
2. _____
3. A teacher finds a paper on the ground in the classroom. When she looks at it carefully she realizes it is from her geometry class because it has a construction on it. Choose all of the following constructions found directly from this student’s work.
A) The midpoint of 𝐴𝐵 B) The perpendicular bisector of 𝐴𝐵
C) A perpendicular line to 𝐴𝐵 D) The angle bisector of CAB
3. _____
4. Which construction is represented by these construction marks?
A) Copying ABC B) The perpendicular bisector of 𝐵𝐶
C) The angle bisector of ABC D) A perpendicular line 𝐴𝐶
4. _____
5. When doing a construction, which geometric instrument is used to measure length? A) A ruler B) A compass C) A protractor D) A straightedge
5. _____
6. Given the diagram, choose all the descriptions that are true. A) The circle is inscribed in the square. B) The triangle is inscribed in the circle. C) The square is inscribed in the circle. D) The circle circumscribes the triangle.
6. _____
7. Jeff is constructing the angle bisector of DBE. What is the next step? Be very specific as to what he should do next. (2 points)
8. When you do a midpoint construction of 𝐶𝐷, you must stretch your compass so that it is greater than half the distance of
𝐶𝐷. Why do you have to do this? Why couldn’t you use a distance smaller than half of 𝐶𝐷? (2 points)
D
EB
B
A
C D E F
BA
D
C
A
B
B
A
C
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Geometry 94
Geometry 94
9. A teacher instructs the class to construct four times the length of a segment. George pulls out his ruler and measures the segment to the nearest millimeter and then multiplies the length by four. He marks this distance from one of the endpoints. Has he done this correctly? Explain. (2 points)
10. George is told that 𝐴𝐵 and 𝐶𝐷 have equal lengths. The student writes down 𝐴𝐵 = 𝐶𝐷. What is wrong with this mathematical statement? (2 points) 11. Use the diagram to complete the relationship. (1 point each) (In diagrams 1, 2 and 4 the compass was constant for each individual construction.)
a) DF = _______
b) 𝐸𝐹 _______
c) CE = _______
d) 𝐸𝐷 _______
e) _______ = _______
f) _______ _______
g) mABF = _______
h) 𝐵𝐸 _______ 12. Complete the following. (2 points each)
a) Provide all correct names for the angle.
b) Draw the perpendicular bisector of
CD . (Completely label the diagram)
c) Draw a circle inscribed in a square d) Draw a hexagon circumscribed about a circle.
13. Construct the following regular polygons. (2 points each)
a) An Equilateral Triangle b) A Square c) A Hexagon
F
D
C
E
E
G
F
C D
F'E'
E FC D
F
D
B
A
CE
3
B
D
H
C
D
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Name _________________ 95
Geometry 95
14. Construct the following. (2 points each)
• A) Construct the perpendicular bisector of 𝐴𝐵
• B) Copy CFG down the ray at F’ (thus creating two parallel lines)
• C) Construct the angle bisector of BCD
• D) Construct the perpendicular line to 𝐶𝐷⃡⃗⃗⃗ ⃗ through point E
• E) Construct the perpendicular line to 𝐶𝐷⃡⃗⃗⃗ ⃗ through point D
• F) On the ray below construct exactly the length 2.5 AB – 2FG
• G) Who is bigger AB or CF + FG + GC? ___________ (Compare them on the ray below)
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Geometry 96
Geometry 96