1. 8-3 Proving Triangles Similar Learning Target: I will be able to prove triangles are similar. Goal 2.03

2. Angle-Angle Similarity (AA~) Postulate If two angles of a triangle are congruent to two angles of another triangle, then the triangles are similar. TRS ~ PLM R T S P M L

3. Using the AA~ Postulate, explain why the triangles are similar. (You can write a proof) W R V B S 45 0 Can you find the similarity ratio? Explain? Angle R is congruent to Angle V. Angle WSR is congruent to Angle BSV because vertical angles are congruent. The two triangles are similar based on the AA Postulate. No, we do not know the side lengths.

4. Side-Angle-Side Similarity (SAS ~) Theorem If an angle of one triangle is congruent to an angle of a second triangle, and the sides including the two angles are proportional, then the triangles are similar.

5. P Q M A B 8 4 4 2 Explain why the triangles are congruent. QM/AM=4/2=2 PM/BM=8/4=2 So, two sides are proportional. Angle QMP is congruent to Angle AMB because vertical angles are congruent. Triangle PQM is similar to Triangle BAM because of SAS Postulate.

6. Side-Side-Side Similarity (SSS~) Theorem If the corresponding sides of two triangles are proportional, then the triangles are similar.

7. Find the value of x. Think about the theorems we just discussed. x 15 8 11 12 10 15 12 = x 11 __ x=13.75