CK-12 Geometry-Concepts

7.6. SSS Similarity http://www.ck12.org

BA

F E=

21

15 =

7

5

AC

ED=

14

10 =

7
5
Since all the ratios are the same, 4 ABC∼4EF Dby the SSS Similarity Theorem.

Example B

Findxandy, such that 4 ABC∼4DEF.

According to the similarity statement, the corresponding sides are:DEAB=EFBC=DFAC. Substituting in what we know,
we have^96 =^4 x 10 −^1 =^18 y.

9

6

=

4 x− 1

10

9

6

=

18

y

9 ( 10 ) = 6 ( 4 x− 1 ) 9 y= 18 ( 6 )

90 = 24 x− 6 9 y= 108

96 = 24 x y= 12

x= 4

Example C

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

We will need to find the ratios for the corresponding sides of the triangles and see if they are all the same. Start with
the longest sides and work down to the shortest sides.
AC
ED=

21

35 =

3

5

BC

F D=

15

25 =

3

5

AB

EF=

10

20 =

1
2
Since the ratios are not all the same, the triangles are not similar.

Watch this video for help with the Examples above.