NAME ______________________________________________ DATE

7-3

____________ PERIOD _____

Study Guide and Intervention Similar Triangles

Identify Similar Triangles

Here are three ways to show that two triangles are similar.

AA Similarity

Two angles of one triangle are congruent to two angles of another triangle.

SSS Similarity

The measures of the corresponding sides of two triangles are proportional.

SAS Similarity

The measures of two sides of one triangle are proportional to the measures of two corresponding sides of another triangle, and the included angles are congruent.

Example 1

Example 2

Determine whether the triangles are similar. 10

A

B 8

6

15

D 9

C

Determine whether the triangles are similar. Q

M

E 3

12

N

F

AC 6 2 !! " !! " !! DF 9 3 8 BC 2 !! " !! " !! 12 EF 3 AB 10 2 !! " !! " !! DE 15 3

70!

4

P

6

R

70!

S

8

3 6 MN NP !! " !!, so !! " !!. 4 8 QR RS

m"N " m"R, so "N " "R. !NMP ! !RQS by SAS Similarity.

!ABC ! !DEF by SSS Similarity.

Determine whether each pair of triangles is similar. Justify your answer. 1.

2.

24 20

18

36

3.

4.

4 8 65!

5.

6.

16

24 39

Chapter 7

21

9

18

32 24

26

65!

20 40

15

25

Glencoe Geometry

Lesson 7-3

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Exercises

NAME ______________________________________________ DATE

7-3

Study Guide and Intervention

____________ PERIOD _____

(continued)

Similar Triangles Use Similar Triangles Example 1 B

A

18

18

D

C

18!# 3

Example 2

!ABC ! !DEF.

Find x and y. y

Similar triangles can be used to find measurements.

AC BC !! " !! DF EF 18!3 " 18 ! " !! x 9

18x " 9(18!3 ") x " 9!3 "

x

A person 6 feet tall casts a 1.5-foot-long shadow at the same time that a flagpole casts a 7-foot-long shadow. How tall is the flagpole?

E 9

F

AB BC !! " ! ! DE EF y 18 ! ! " !! 18 9

? 6 ft 1.5 ft

7 ft

The sun’s rays form similar triangles. 6 1.5 Using x for the height of the pole, !! " !!, x 7 so 1.5x " 42 and x " 28. The flagpole is 28 feet tall.

9y " 324 y " 36

Exercises Each pair of triangles is similar. Find x and y. 1.

2. 10

35

13

x!2 20

20

13

4.

36!# 2 y

x 36

5.

38.6 30

y 8

x

y

6.

9

60

23

24 36

10 30

x

7.2

y

26

x

3.

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

y

32

16

22

y x

7. The heights of two vertical posts are 2 meters and 0.45 meter. When the shorter post casts a shadow that is 0.85 meter long, what is the length of the longer post’s shadow to the nearest hundredth? Chapter 7

22

Glencoe Geometry