1. 6.5 Prove Triangles Similar by SSS and SAS
Hubarth
Geometry

2. Side-side-side Similarity Theorem (SSS)~ A F G H C B

3. Ex 1. Use the SSS Similarity Theorem
Determine whether the triangles are similar. If they are similar, write a similarity statement
and find the scale factor of Triangle B to Triangle A. P S B 6 4 B 8 12 A T U 5 R Q 10
Solution

4. Ex 2. Use the SSS Similarity Theorem12 14 A C E G J 6 4 6 6 9 10 D F 8 H B
Solution

5. Ex 3 Use the SSS Similarity Theorem
Find the value of x that makes corresponding side lengths proportional.
DF = 3(x + 1) = 24 4 12 =
x –1 18 AB DE AC DF = ? 8 24 4 12 =
= 12(x – 1)
72 = 12x – 12
7 = x

6. Side-Angle-Side Similarity Theorem (SAS)X M P N Z Y

7. Shorter sides Longer sides Ex 4 Use the SAS Similarity Theorem
You are building a lean-to shelter starting from a tree branch, as shown. Can you construct the right end so it is similar to the left end using the angle measure and lengths shown?
Both m A and m F equal = 53°, so A F. Next, compare the ratios of the lengths of the sides that include A and F.
Shorter sides
Longer sides AB FG 3 2 9 6 = AC FH 3 2 15 10 =
So, by the SAS Similarity Theorem, ABC ~ FGH. Yes, you can make the right end similar to the left end of the shelter.

8. Shorter sides Longer sides Ex 5 Choose a Method
Tell what method you would use to show that the triangles are similar.
Find the ratios of the lengths of the corresponding sides.
Shorter sides
Longer sides BC EC 3 5 9 15 = CA CD 3 5 18 30 =
The corresponding side lengths are proportional. The included angles ACB and DCE are congruent because they are vertical angles. So, ACB ~ DCE by the SAS Similarity Theorem.

9. Practice
1. Determine whether the triangles are similar. If they are similar, write a similarity
statement. J A 15 10 R D A. B F B. 12 12 13 8 18 15 12 12 E K L C 5 S T 9
2. Determine whether the triangles are similar. If they are similar, write a similarity
statement. Explain your reasoning. P 5 3 Q R 3 5 S T