Chapter 7 Quiz ReviewChapter 7 Quiz Review

Lessons 7.1-7.3Lessons 7.1-7.3

You need to know:You need to know:

How to write and reduce a ratioHow to write and reduce a ratio How to write and solve a proportionHow to write and solve a proportion How to write a similarity statement, find a How to write a similarity statement, find a

scale factor, and find x or y in a set of scale factor, and find x or y in a set of similar polygonssimilar polygons

How to determine if two triangles or other How to determine if two triangles or other polygons are similar and justify your polygons are similar and justify your answer (corresponding sides are answer (corresponding sides are proportional and corresponding angles are proportional and corresponding angles are congruent or for triangles: AA Similarity, congruent or for triangles: AA Similarity, SAS Similarity, or SSS Similarity)SAS Similarity, or SSS Similarity)

1a. Find x and the length of each 1a. Find x and the length of each side of the triangle.side of the triangle.

The three sides of a triangle are in the The three sides of a triangle are in the ratio 2:4:5. The perimeter of the ratio 2:4:5. The perimeter of the triangle is 253cm. triangle is 253cm.

1b. Find x and the length of each 1b. Find x and the length of each side of the triangle.side of the triangle.

The three angles of a triangle are in The three angles of a triangle are in the ratio 4:5:6. Find the measure of the ratio 4:5:6. Find the measure of

each angle.each angle.

2. Solve the Proportion2. Solve the Proportion

9

2

6

5 x

3. Solve the Proportion3. Solve the Proportion

6

7

4

7

x

x

4. Determine if the polygons are 4. Determine if the polygons are similar. Write a similarity statement similar. Write a similarity statement

and find the scale factor.and find the scale factor.

131°

76°

10°

16.816.6

16.3

D

E FF

131°

76°

10°

16.8

16.6

16.3C A

B

5. Determine if the triangles are 5. Determine if the triangles are similar. Write a similarity statement, similar. Write a similarity statement,

find the scale factor, and find x.find the scale factor, and find x.

46° 75°

59°

7.6

6.3 5.7

E F

D

46°

75°59°

x

21.66

C

B

A

6. The quadrilaterals are similar, 6. The quadrilaterals are similar, find x and CB.find x and CB.

58° 128°

82°

7.2

6.4

3.6

E F

H

G

7.8

73°

58°

128°

82°

x

28.08

C

B

A

– 2

D

73°

7. Determine if the triangles are 7. Determine if the triangles are similar, justify your answer.similar, justify your answer.

10

9 8

E F

D 24

C

B

A

2730

8. Determine if the triangles are 8. Determine if the triangles are similar, justify your answer.similar, justify your answer.

9. Find x, AB and BC.9. Find x, AB and BC.

10. Find x, BC, and AC10. Find x, BC, and AC

Answers:Answers:

1a. 2x + 4x + 5x = 1a. 2x + 4x + 5x = 253253

11x = 25311x = 253 x = 23x = 23 46cm, 92cm, 115cm46cm, 92cm, 115cm

1b. 4x + 5x + 6x = 1801b. 4x + 5x + 6x = 180 15x = 18015x = 180 x = 12x = 12 48, 60, 72 degrees48, 60, 72 degrees

2. 5x9 = 6(x + 2)2. 5x9 = 6(x + 2)

45 = 6x + 1245 = 6x + 12

33 = 6x33 = 6x

x = 5.5x = 5.5

Answers:Answers:

3. 6(x + 7) = 7(x + 3. 6(x + 7) = 7(x + 4)4)

6x + 42 = 7x + 6x + 42 = 7x + 2828

42 = x + 2842 = x + 28

x = 14x = 14

4. 4. Triangle ABC~Triangle Triangle ABC~Triangle EDFEDF

scale factor = 1/1 scale factor = 1/1

Answers:Answers:

5. Yes they are 5. Yes they are similar by AA similar by AA Similarity.Similarity.

scale factor= scale factor=

6. 6.

66.21

7.5

94.23

458.1367.5

3.6

66.21

7.5

x

xx

04.23

04.25

312.1958.7

712.1796.158.72

4.6

08.28

8.7

CB

x

x

xx

Answers:Answers:

7. Yes by SSS 7. Yes by SSS similarity.similarity.

8. Yes by SAS 8. Yes by SAS Similarity.Similarity.

(all corresponding (all corresponding sides are in a ratio sides are in a ratio of 1/1)of 1/1)

3

1

30

103

1

27

93

1

24

8

Answers:Answers:

9. 9. 10. 10.

8

14

5

2116

21716842

3

7

4

BC

AB

x

x

xxx

x

12

10

6

6122

6

1

6

AC

BC

x

x

x