CK-12 Geometry Concepts

http://www.ck12.org Chapter 7. Similarity

Vocabulary

Two triangles aresimilarif all their corresponding angles arecongruent(exactly the same) and their corresponding
sides areproportional(in the same ratio).

Guided Practice

Determine if the following triangles are similar. If so, write the similarity theorem and statement.

Answers:

1. We can see that^6 B∼=^6 Fand these are both included angles. We just have to check that the sides around the
   angles are proportional.
   AB
   DF=

12

8 =

3

2

BC

F E=

24

16 =

3

2

Since the ratios are the same 4 ABC∼4DF Eby the SAS Similarity Theorem.

2. The triangles are not similar because the angle is not the included angle for both triangles.
   3.^6 Ais the included angle for both triangles, so we have a pair of congruent angles. Now we have to check that the
   sides around the angles are proportional.
   AE
   AD=

16

16 + 4 =

16

20 =

4

5

AB

AC=

24

24 + 8 =

24

32 =

3
4
The ratios are not the same so the triangles are not similar.

Practice

Fill in the blanks.

1. If two sides in one triangle are to two sides in another and the ____ angles
   are , then the triangles are __.

Determine if the following triangles are similar. If so, write the similarity theorem and statement.

2.

Find the value of the missing variable(s) that makes the two triangles similar.

3.

4.

5.

Determine if the triangles are similar.

6.∆ABCis a right triangle with legs that measure 3 and 4.∆DEFis a right triangle with legs that measure 6 and

8.