Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Geometry - Review for Final Chapters 3 and 4

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. In the diagram, c Ä d . Identify three numbered angles that have a measure of 124°.

a. ∠2, ∠7, and ∠1 c. ∠3, ∠7, and ∠4b. ∠2, ∠4, and ∠1 d. ∠2, ∠3, and ∠7

____ 2. In the diagram, b Ä c. Find the value of y.

a. 70 c. 36b. 54 d. 20

Name: ________________________ ID: A

2

____ 3. Find the distance from point P to RQ.

a. about 3.2 units c. 10 unitsb. 4 units d. about 2.8 units

____ 4. Which two lines must be parallel in the diagram?

a. m Ä n c. j Ä kb. l Ä m d. n Ä l

Name: ________________________ ID: A

3

In the diagram, think of each segment in the figure as part of a line.

____ 5. Name the line(s) through point D that appear parallel to HG→←

.

a. DH→←

c. DC→←

and AD→←

b. DC→←

d. DG→←

____ 6. Name the line(s) through point B that appear skew to HG→←

.

a. BC→←

c. BF→←

b. BC→←

and BA→←

d. BC→←

and BF→←

____ 7. Name the line through point D that appears perpendicular to HG→←

.

a. DG→←

c. DH→←

b. DC→←

d. AD→←

____ 8. Name the plane through point A that appears parallel to EFG.a. ABC c. AEHb. AEF

____ 9. Classify the pair of numbered angles.

a. corresponding c. alternate interiorb. alternate exterior d. consecutive interior

Name: ________________________ ID: A

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____ 10. Classify the pair of numbered angles.

a. corresponding c. alternate interiorb. alternate exterior d. consecutive interior

____ 11. Classify the pair of numbered angles.

a. corresponding c. alternate interiorb. alternate exterior d. consecutive interior

Name: ________________________ ID: A

5

____ 12. Graph CD with endpoints C(–8, 2) and D(–5, 6) and its image after the composition.

Translation: x,yÊËÁÁ

ˆ¯̃̃ → x + 1, y − 3Ê

ËÁÁˆ¯̃̃

Translation: x,yÊËÁÁ

ˆ¯̃̃ → x + 2, y + 2Ê

ËÁÁˆ¯̃̃

a. c.

b. d.

Name: ________________________ ID: A

6

____ 13. Graph BCD with vertices B(2, 1), C(4, 4) and D(4, 1) and its image after the reflection in the line n: x = 1.

a. c.

b. d.

Name: ________________________ ID: A

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____ 14. The vertices of DEF are D(–3, –3), E(–2, –4), and F(–2, 0). Graph DEF and its image after the reflection in the line y = −x .

a. c.

b. d.

Name: ________________________ ID: A

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____ 15. Graph ABC with vertices A(–6, 2), B(–2, 2) and C(0, 1) and its image after the glide reflection.

Translation: x, yÊËÁÁ

ˆ¯̃̃ → x + 3, yÊ

ËÁÁˆ¯̃̃

Reflection: in the x-axis

a. c.

b. d.

Name: ________________________ ID: A

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____ 16. How many lines of symmetry does the rhombus have?

a. 1 c. 2b. 4 d. none

____ 17. Graph the polygon and its image after a rotation of 270° counterclockwise about the origin.

a. c.

b. d.

Name: ________________________ ID: A

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____ 18. A railway turntable is used to turn locomotives around or quickly change their direction in small spaces. A locomotive enters the turntable on track 2, is rotated 180° counterclockwise, and exits the turntable. What track does the train leave on?

a. Track 4 c. Track 1b. Track 2 d. Track 3

____ 19. An image of a celebrity is going to be used on a promotional billboard. The person is 6.25 feet tall in real life, and 21.875 feet tall on the billboard. What is the scale factor of this dilation?a. 0.29 c. 14.0625b. 15.625 d. 3.5

Name: ________________________ ID: A

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____ 20. Describe the similarity transformation that maps WXY to ABC (dilations have a center at the origin).

a. dilation with a scale factor of 13

followed by a reflection in the y-axis

b. dilation with a scale factor of 13

followed by a reflection in the x-axis

c. dilation with a scale factor of 3 followed by a reflection in the y-axisd. dilation with a scale factor of 3 followed by a reflection in the x-axis

____ 21. Describe the similarity transformation that maps ABC to RST (dilations have a center at the origin).

a. rotation 180° about the origin followed by a dilation with a scale factor of 3b. rotation 90° counterclockwise about the origin followed by a dilation with a scale factor

of 13

c. rotation 180° about the origin followed by a dilation with a scale factor of 13

d. rotation 90° counterclockwise about the origin followed by a dilation with a scale factor of 3

Name: ________________________ ID: A

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____ 22. In the diagram, BC→←

bisects ∠ACD and j Ä k . Find the value of w.

a. 67 c. 58b. –22 d. –13

____ 23. Find the value of x that makes j Ä k .

a. 44 c. 42b. 46 d. 40

____ 24. Find the value of x that makes a Ä b.

a. 130 c. 15b. 50 d. 55

Name: ________________________ ID: A

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____ 25. The diagram represents the streets of the downtown area of a city. Determine which lines, if any, must be parallel in the diagram.

a. u Ä t c. s Ä ub. a Ä b d. none

____ 26. Write a rule for the translation of ABC to A′B′C ′.

a. x,yÊËÁÁ

ˆ¯̃̃ → x − 1, y − 3Ê

ËÁÁˆ¯̃̃ c. x,yÊ

ËÁÁˆ¯̃̃ → x, y + 2Ê

ËÁÁˆ¯̃̃

b. x,yÊËÁÁ

ˆ¯̃̃ → x + 2, yÊ

ËÁÁˆ¯̃̃ d. x,yÊ

ËÁÁˆ¯̃̃ → x + 3, y + 2Ê

ËÁÁˆ¯̃̃

Name: ________________________ ID: A

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____ 27. In the diagram, the figure is reflected in line a. The image is then reflected in line b. Describe a single transformation that maps F to F ″.

a. 90° rotation about point J c. 22° rotation about point Jb. 88° rotation about point J d. 134° rotation about point J

____ 28. Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement.

a.25

; reduction c.23

; reduction

b.52

; enlargement d.32

; enlargement

Name: ________________________ ID: A

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____ 29. In the diagram, name the vector and select its component form.

a. AO→

, −4,−1 c. AO→

, −1,−4

b. OA→

, 4,1 d. OA→

, 1,4

Multiple ResponseIdentify one or more choices that best complete the statement or answer the question.

____ 1. Which statements are enough to conclude that m Ä n?

a. ∠6 ≅ ∠3 c. ∠1 ≅ ∠9b. ∠1 and ∠7 are supplementary. d. ∠1 ≅ ∠12

Name: ________________________ ID: A

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____ 2. In the diagram, k Ä j, AB is reflected in line k, A′B′ is reflected in line j, AA′ = 6 centimeters, and the distance from A′ to line j is 12 centimeters. Which of the following statements are true?

a. The distance from A to line k is 3 centimeters. b. BB″ = 30 cm

c. B′B″⊥ line j

d. A rotation maps AB onto A″B″.

Short Answer

1. Describe the similarity transformation that maps ABC to DEF (dilations have a center at the origin).

2. Write an equation of the line passing through the point (3, 0) that is parallel to the line 2x + 3y = 9.

3. Write an equation of the line passing through the point (- 1, 6) that is perpendicular to the line y = −13

x + 5.

Name: ________________________ ID: A

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4. Graph ST with endpoints at S 4,1ÊËÁÁ

ˆ¯̃̃ and T −4,0Ê

ËÁÁˆ¯̃̃ and its image after the composition.

Rotation: 270° counterclockwise about the originReflection: in the line y = −x

5. Graph the polygon and its image after the reflection in the line y = x .

6. Graph ST with endpoints at S −3,0ÊËÁÁ

ˆ¯̃̃ and T 1,−1Ê

ËÁÁˆ¯̃̃ and its image after the composition.

Translation: x, yÊËÁÁ

ˆ¯̃̃ → x − 2, y + 2Ê

ËÁÁˆ¯̃̃

Rotation: 180° about the origin

7. Graph RST with vertices at R 1,3ÊËÁÁ

ˆ¯̃̃ , S −1,−2Ê

ËÁÁˆ¯̃̃ and T 4,0Ê

ËÁÁˆ¯̃̃ and its image after the composition.

Reflection: in the x-axisRotation: 90° counterclockwise about the origin

8. Graph quadrilateral ABCD with vertices A 4,−8ÊËÁÁ

ˆ¯̃̃ , B −2,8Ê

ËÁÁˆ¯̃̃ , C −8,2Ê

ËÁÁˆ¯̃̃ and D −6,−4Ê

ËÁÁˆ¯̃̃ and its image after a

dilation centered at (0, 0) with a scale factor of –0.5.

9. Graph ABC with vertices A −2,3ÊËÁÁ

ˆ¯̃̃ , B 0,−4Ê

ËÁÁˆ¯̃̃ , and C 2,0Ê

ËÁÁˆ¯̃̃ and its image after the similarity transformation.

Translation: x, yÊËÁÁ

ˆ¯̃̃ → x + 3, y − 2Ê

ËÁÁˆ¯̃̃

Dilation: x, yÊËÁÁ

ˆ¯̃̃ → 1.5x, 1.5yÊ

ËÁÁˆ¯̃̃

Name: ________________________ ID: A

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Other

The given line markings show how the roads in a town are related to one another.

1. Can you use the Perpendicular Postulate to show that BD→←

is not perpendicular to AB→←

? Explain why or why not.

2. Can you use the Parallel Postulate to show that AB→←

is not parallel to AD→

? Explain why or why not.

3. In the Malaysian flag, each stripe is parallel to the stripe immediately below it. Explain why the top stripe is parallel to the bottom stripe.

Name: ________________________ ID: A

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4. In the diagram of the parking lot, m∠1 = 60°. What is m∠2? How do you know?

5. A helicopter pilot sees an island at a 70° angle of depression from the horizontal. In the diagram, m∠1 = 70°. What is m∠2? How do you know?

ID: A

1

Geometry - Review for Final Chapters 3 and 4Answer Section

MULTIPLE CHOICE

1. D 2. C 3. D 4. A 5. B 6. D 7. C 8. A 9. B 10. A 11. D 12. A 13. B 14. A 15. D 16. C 17. B 18. B 19. D 20. A 21. C 22. D 23. C 24. B 25. A 26. B 27. B 28. A 29. D

MULTIPLE RESPONSE

1. A, B 2. A, B, C

SHORT ANSWER

1. translation 4 units right and 3 units down followed by a dilation with a scale factor of 2 2. y = - 2/3x + 2

ID: A

2

3. y = 3x + 9

4.

5.

6. S ′ −5,2ÊËÁÁ

ˆ¯̃̃ ,T

′ −1,1ÊËÁÁ

ˆ¯̃̃

S ″ 5,−2ÊËÁÁ

ˆ¯̃̃ ,T

″ 1,−1ÊËÁÁ

ˆ¯̃̃

ID: A

3

7. R′ 1,−3Ê

ËÁÁˆ¯̃̃,S

′ −1,2ÊËÁÁ

ˆ¯̃̃ ,T

′ 4,0ÊËÁÁ

ˆ¯̃̃

R″ 3,1ÊËÁÁ

ˆ¯̃̃ ,S

″ −2,−1ÊËÁÁ

ˆ¯̃̃,T

″ 0,4ÊËÁÁ

ˆ¯̃̃

8.

A′ −2,4ÊËÁÁ

ˆ¯̃̃ , B′ 1,−4Ê

ËÁÁˆ¯̃̃ , C ′ 4,−1Ê

ËÁÁˆ¯̃̃ , D 3,2Ê

ËÁÁˆ¯̃̃

ID: A

4

9. A′ 1,1ÊËÁÁ

ˆ¯̃̃,B

′ 3,−6ÊËÁÁ

ˆ¯̃̃ ,C

′ 5,−2ÊËÁÁ

ˆ¯̃̃

A″ 1.5,1.5ÊËÁÁ

ˆ¯̃̃ ,B

″ 4.5,−9ÊËÁÁ

ˆ¯̃̃ ,C

″ 7.5,−3ÊËÁÁ

ˆ¯̃̃

OTHER

1. no; D does not lie on AB→←

, but there is no way to determine whether BD→←

is the one line perpendicular to AB→←

through D. A does not lie on BD→←

, but there is no way to determine whether AB→←

is the one line perpendicular

to BD→←

through A.

2. yes; Because BF→

is parallel to AD→

, AB→←

could not also be parallel to AD→

through B according to the Parallel Postulate.

3. By The Transitive Property of Parallel Lines, the top stripe is parallel to the bottom stripe. 4. m∠2 = 60°; Alternate Exterior Angles Theorem 5. m∠2 = 70°; Alternate Interior Angles Theorem

ID: A Geometry - Review for Final Chapters 3 and 4 [Answer Strip]

_______ 1.D

_______ 2.C

_______ 3.D

_______ 4.A

_______ 5.B

_______ 6.D

_______ 7.C

_______ 8.A

_______ 9.B

_______10.A

_______11.D

ID: A Geometry - Review for Final Chapters 3 and 4 [Answer Strip]

_______12.A _______13.B _______14.A _______15.D

ID: A Geometry - Review for Final Chapters 3 and 4 [Answer Strip]

_______16.C

_______17.B

_______18.B

_______19.D

_______20.A

_______21.C

_______22.D

_______23.C

_______24.B

ID: A Geometry - Review for Final Chapters 3 and 4 [Answer Strip]

_______25.A

_______26.B

_______27.B

_______28.A

_______29.D

_______ 1.A, B

_______ 2.A, B, C