NAME: 6/5 t SIMILARITY, CONGRUENCE, AND PROOFS Lesson 1: Investigating Properties …rbeasleymath.weebly.com/uploads/2/1/0/6/21068448/... · 2019-08-06 · 6/5 t similarity, congruence,

Unit2Review

2.

SIMILARITY, CONGRUENCE, AND PROOFSLesson 1: Investigating Properties of Dilations

NAME:

Assessment

CCGPS Analytic Geometry Teacher Resource © Walch EducationU1-1

continued

Circle the letter of the best answer.

1. Does the graph below represent a dilation? Why or why not?

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

-10-9-8-7-6-5-4-3-2-1

123456789

10

D (0, 7)

E (5, 7)

F (5, 0)

D (0, 3.5)

C

E

y

x

(5, 3.5)

a. Yes, because the preimage sides are parallel with the corresponding image sides.

b. No, because the preimage sides are not parallel with the corresponding image sides.

c. Yes, because there is a single scale factor and a center of dilation.

d. No, because the scale factors of the image sides are not all consistent with the preimage sides.

Pre-Assessment


NAME:

Assessment

CCGPS Analytic Geometry Teacher Resource U1-2

© Walch Education

2. Determine the scale factor of the dilation below.

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

-10-9-8-7-6-5-4-3-2-1

123456789

10

D (–4, 4)

E (4, 4)

D (–2, 2)

C

E(2, 2)

y

x

a. k = 2

b. 1

4k =

c. 1

2k =

d. k = 1

3. Determine the scale factor of the dilation below.

3.75

12.9C

1.5

34.532.25G

H

J

G

H

J

13.8

a. k = 1.07

b. k = 2.5

c. k = 0.4

d. k = 9.2 continued

3.

4.

5.

6.

7.


NAME:

Assessment


4. AB is 6.7 units long. If AB is dilated by a scale factor of k = 3.2, what is the length of A B′ ′ ?

a. 21.4 units

b. 2.1 units

c. 0.5 unit

d. 1 unit

5. -FGH has vertices F (3, –5), G (8, –6), and H (6, –7). If -FGH is dilated through the origin

with a scale factor of 3

4, what are the vertices of -F G H′ ′ ′?

a. F' (–3, 5), G' (–8, 6), and H' (–6, 7)

b. F' (2.25, –3.75), G' (6, –4.5), and H' (4.5, –5.25)

c. 4,20

3F ′⎛⎝⎜

⎞⎠⎟

, 32

3, –8G′

⎛⎝⎜

⎞⎠⎟

, and 8,28

3H ′ −

⎛⎝⎜

⎞⎠⎟

d. F' (–5, 3), G' (–6, –8), and H' (–7, 6)

SIMILARITY, CONGRUENCE, AND PROOFSLesson 5: Congruent Triangles

NAME:

Assessment


Pre-AssessmentCircle the letter of the best answer.

1. UVW- and XYZ- are congruent triangles. Which statement is known to be true?

a. ∠ ≅∠U V

b. ∠ ≅∠W X

c. ∠ ≅∠V X

d. ∠ ≅∠V Y

2. ABC- and DEF- are congruent triangles. Which statement is known to be true?

a. ≅AB BC

b. ≅AB EF

c. ≅AC DF

d. ≅AB DF

3. A triangle congruent to ABC- is to be constructed. Only three components are measured. Which three components, if constructed in the order listed, will always create a congruent triangle?

a. side-side-angle

b. angle-angle-angle

c. angle-side-angle

d. Only the three side lengths can be used to create a congruent triangle.

4. Which set of equivalent measures does not indicate that two triangles must be congruent?

a. angle-angle-angle

b. angle-side-angle

c. side-angle-side

d. angle-angle-side

5. For ABC- and DEF- , the following is given: ∠ ≅∠A D , ∠ ≅∠B E , ∠ ≅∠C F . By which triangle congruence statement can it be concluded that the triangles are congruent?

a. SSS

b. SAS

c. ASA

d. It cannot be determined if the triangles are congruent.


NAME:

Assessment




a. ∠ ≅∠U V

b. ∠ ≅∠W X

c. ∠ ≅∠V X

d. ∠ ≅∠V Y


a. ≅AB BC

b. ≅AB EF

c. ≅AC DF

d. ≅AB DF


a. side-side-angle


c. angle-side-angle




b. angle-side-angle

c. side-angle-side

d. angle-angle-side


a. SSS

b. SAS

c. ASA

d. It cannot be determined if the triangles are congruent.


NAME:

Assessment




a. ∠ ≅∠U V

b. ∠ ≅∠W X

c. ∠ ≅∠V X

d. ∠ ≅∠V Y


a. ≅AB BC

b. ≅AB EF

c. ≅AC DF

d. ≅AB DF


a. side-side-angle


c. angle-side-angle




b. angle-side-angle

c. side-angle-side

d. angle-angle-side


a. SSS

b. SAS

c. ASA

d. It cannot be determined if the triangles are congruent.SIMILARITY, CONGRUENCE, AND PROOFS

Lesson 6: Defining and Applying Similarity

NAME:

Assessment


2. ABC- has undergone a series of similarity transformations to produce EFG- . Which of the following statements is NOT true?

a. The angles of EFG- are proportional to the angles of ABC- .

b. The angles of EFG- are the same as the angles of ABC- .

c. The sides of EFG- are proportional to the sides of ABC- .

d. ABC- is similar to EFG- .

3. What is the length of EF ?D

E

F

92

4.5A

B

C

a. 4 units

b. 1 unit

c. 9 units

d. 2 units

4. Are the two triangles similar? Why or why not?

B

CA

E

FD

a. Yes, they are similar because of the AA Similarity Statement.

b. Yes, they are similar because of the ASA Congruence Statement.

c. No, they are not similar because they are congruent.

d. There is not enough information to determine similarity.

continued

8.

9.

10.

SIMILARITY, CONGRUENCE, AND PROOFSLesson 6: Defining and Applying Similarity

NAME:

Assessment








E

F

92

4.5A

B

C

a. 4 units

b. 1 unit

c. 9 units

d. 2 units


B

CA

E

FD





continued


NAME:

Assessment








E

F

92

4.5A

B

C

a. 4 units

b. 1 unit

c. 9 units

d. 2 units


B

CA

E

FD





continued


NAME:

Assessment


© Walch Education

5. Identify the similar triangles. Find x and the missing side lengths.

B

A

C

D

E

x + 5

10

x + 12.53

6

4

a. ABC CDE△ ∼△ ; x = 2.5; DC = 7.5; EC = 15

b. ABC DEC△ ∼△ ; x = 2.5; DC = 15; EC = 7.5

c. ABC DEC△ ∼△ ; x = 2.5; DC = 7.5; EC = 15

d. ABC DEC△ ∼△ ; x = 5.2; DC = 10.5; EC = 18

11.

12.

13.

SIMILARITY, CONGRUENCE, AND PROOFSLesson 7: Proving Similarity

NAME:

Assessment


© Walch Education

continued


1. The length of a building’s shadow is 107.2 feet. At the same time of day, a 1.8-foot-tall tree casts a shadow that is 2.4 feet long. What is the height of the building?

a. 80.4 feet

b. 142.9 feet

c. 24.8 feet

d. 463.1 feet

2. △ ∼△ABC DEC . What is the length of EC ?

A

D E

C

B

15 10

6 x

a. 25 units

b. 9 units

c. 4 units

d. There is not enough information to determine the length of EC .

3. In -ABC , the bisector of ∠A divides BC into segments with lengths of 24 units and 30 units. If AC = 37.5 units, what could be the length of AB ?

a. 46.875 units

b. 30 units

c. 19.2 units

d. There is not enough information to determine the length of AB .

Pre-Assessment


NAME:

Assessment


© Walch Education

continued


1. The length of a building’s shadow is 107.2 feet. At the same time of day, a 1.8-foot-tall tree casts a shadow that is 2.4 feet long. What is the height of the building?

a. 80.4 feet

b. 142.9 feet

c. 24.8 feet

d. 463.1 feet

2. △ ∼△ABC DEC . What is the length of EC ?

A

D E

C

B

15 10

6 x

a. 25 units

b. 9 units

c. 4 units

d. There is not enough information to determine the length of EC .

3. In -ABC , the bisector of ∠A divides BC into segments with lengths of 24 units and 30 units. If AC = 37.5 units, what could be the length of AB ?

a. 46.875 units

b. 30 units

c. 19.2 units

d. There is not enough information to determine the length of AB .

Pre-Assessment


NAME:

Assessment


4. -ABC is a right triangle. Find the length of x, which is the altitude of -ABC .

A C

B

D

x

50

18

a. 30 units

b. 7.7 units

c. 2.7 units

d. There is not enough information to determine the length of x.

5. Which statement would justify that △ ∼△ACE BCD ?

C

D

E

A

B3

7.5

8.75

2.5

a. Angle-Angle (AA) Similarity Statement

b. Side-Angle-Side (SAS) Similarity Statement

c. Side-Side-Side (SSS) Similarity Statement

d. It is not possible to determine if △ ∼△ACE BCD .

14.

15.


NAME:

Assessment


4. -ABC is a right triangle. Find the length of x, which is the altitude of -ABC .

A C

B

D

x

50

18

a. 30 units

b. 7.7 units

c. 2.7 units

d. There is not enough information to determine the length of x.

5. Which statement would justify that △ ∼△ACE BCD ?

C

D

E

A

B3

7.5

8.75

2.5

a. Angle-Angle (AA) Similarity Statement

b. Side-Angle-Side (SAS) Similarity Statement

c. Side-Side-Side (SSS) Similarity Statement

d. It is not possible to determine if △ ∼△ACE BCD .


NAME:

Assessment


© Walch Education

7. What is the length of BD ?

B

C

A

D

20

1030

x

a. 5 units

b. 10 units

c. 20 units

d. There is not enough information to determine the length of BD .

8. -ABC is a right triangle. Find the length of x, the altitude of -ABC .

BC

A

18x

D6

a. 54 units

b. 6 3 units

c. 3 6 units

d. There is not enough information to determine the length of x. continued

16.

17.


NAME:

Assessment


© Walch Education

4. △ ∼△ABF ACE . What is the length of CB ?

B

C

EA F

12

9 5.4

x

a. 7.2 units

b. 4.05 units

c. 20 units

d. There is not enough information to determine the length of CB .

5. △ ∼△ABD ECD . What is the length of CD ?

A DE

C

B

6 18

30

x

a. 90 units

b. 7.5 units

c. 22.5 units

d. There is not enough information to determine the length of CD .

continued

SIMILARITY, CONGRUENCE, AND PROOFSLesson 8: Proving Theorems About Lines and Angles

NAME:

Assessment


© Walch Education


1. In the diagram below, 1∠ and 2∠ are a linear pair. Find m 1∠ if m x1 2 9∠ = − and m x2 10 9∠ = + .

1

2

a. 17º

b. 159º

c. 163º

d. 21º

2. Find m 4∠ in the diagram below if m x2 9( 6)∠ = + and m x4 2(5 21)∠ = + .

1

2

3

4

a. 18º

b. 157º

c. 162º

d. 12º continued

18.

19.


NAME:

Assessment


3. In the diagram below, l is the transversal of the parallel lines m and n. Find m 3∠ if m x4 5( 11)∠ = + and m x5 11 17∠ = − .

1 23 4

5 67 8

l

m

n

a. 115º

b. 65º

c. 78º

d. 12º

4. In the diagram below, l is the transversal of the parallel lines m and n. Find m 8∠ if m x2 3 46∠ = + and m x8 4∠ = .

1 23 4

5 67 8

l

m

n

a. 24º

b. 6º

c. 156º

d. 46º continued


NAME:

Assessment


© Walch Education

5. In the diagram below, l is the transversal of the parallel lines m and n. Find m 5∠ if m x3 2(3 4)∠ = − and m x5 5(3 4)∠ = + .

1 23 4

5 67 8

l

m

n

a. 8º

b. 172º

c. 40º

d. 140º

20.

21.

SIMILARITY, CONGRUENCE, AND PROOFSLesson 9: Proving Theorems About Triangles

NAME:

Assessment


continued


1. What is the measure of ∠B?

a. 45˚

b. 63˚

c. 108˚

d. 117˚

2. What is the measure of ∠C?

40˚A

B

C

D

a. 20˚

b. 40˚

c. 80˚

d. 100˚

Pre-Assessment


NAME:

Assessment


continued


1. What is the measure of ∠B?

a. 45˚

b. 63˚

c. 108˚

d. 117˚

2. What is the measure of ∠C?

40˚A

B

C

D

a. 20˚

b. 40˚

c. 80˚

d. 100˚

Pre-Assessment

22.23.

24.

25.

SIMILARITY, CONGRUENCE, AND PROOFSLesson 10: Proving Theorems About Parallelograms

NAME:

Assessment



1. Determine whether these four vertices form a parallelogram: A (–3, 0), B (6, 0), C (1, 1), D (–2, –2).

a. No, because both pairs of opposite sides are not parallel.

b. Yes, because both pairs of opposite sides are parallel.

c. No, because the diagonals bisect each other.

d. Yes, because the diagonals bisect each other.

2. Determine whether these four vertices form a parallelogram: S (–7, 3), T (–1, 3), U (–2, 1), V (–8, 1).



c. No, because both pairs of opposite sides are not congruent.

d. Yes, because both pairs of opposite sides are not congruent.

3. Classify a quadrilateral as precisely as possible given four vertices: P (–6, –3), Q (–3, –7), R (–7, –10), S (–10, –6).

a. square

b. rhombus

c. trapezoid

d. kite

4. Classify a quadrilateral as precisely as possible given four vertices: D (–5, 2), E (–2, –3), F (8, 3), G (5, 8).

a. square

b. kite

c. isosceles trapezoid

d. rectangle

5. What is always true about rhombuses?

a. The diagonals are not congruent.

b. Two pairs of adjacent distinct sides are congruent.

c. The diagonals intersect at right angles.

d. Every angle measures 90º.

Pre-Assessment


NAME:

Assessment














a. square

b. rhombus

c. trapezoid

d. kite


a. square

b. kite


d. rectangle






Pre-Assessment


NAME:

Assessment


© Walch Education

3. If BC = 3x – 1 and XY = 2x – 3, what is the length of XY?

A

B

C

X

Y

Z

(3x – 1)

(2x – 3)

a. 5 units

b. 7 units

c. 14 units

d. 28 units

4. Which centers of a triangle must be inside the triangle?

a. centroid and incenter

b. circumcenter and incenter

c. centroid and orthocenter

d. orthocenter and incenter

continued


NAME:

Assessment














a. square

b. rhombus

c. trapezoid

d. kite


a. square

b. kite


d. rectangle






Pre-Assessment

Documents

NAME: 6/*5 t SIMILARITY, CONGRUENCE, AND PROOFS Lesson 1: Investigating Properties …rbeasleymath.weebly.com/uploads/2/1/0/6/21068448/... · 2019-08-06 · 6/*5 t similarity, congruence,

NAME: 6/5 t SIMILARITY, CONGRUENCE, AND PROOFS Lesson 1: Investigating Properties …rbeasleymath.weebly.com/uploads/2/1/0/6/21068448/... · 2019-08-06 · 6/5 t similarity, congruence,