# 7 3 Proving Triangles Similar Ways to show

• Slides: 9

7. 3 Proving Triangles Similar

Ways to show triangles are similar � There are 3 ways to show two triangles are similar to each other. Those 3 ways are: 1. Angle-Angle Similarity Postulate. (AA~) 2. Side-Angle-Side Similarity Theorem. (SAS~) 3. Side-Side Similarity Theorem. (SSS~)

Angle-Angle Similarity Postulate If If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Then

Side-Angle-Side Similarity Theorem If an angle of one triangle is congruent to an angle of a second triangle, and the sides that include the two angles are proportional, then the triangles are similar. If Then

Side-Side Similarity Theorem If If corresponding sides of two triangles are proportional, then the triangles are similar. Then

Example � Are the two triangles similar, how do you know? 31° 59° The two triangles are similar by the AA~ postulate. Find the 3 rd angle in one of the triangles to see if it is congruent to the other triangle.

Example � Are the two triangles similar, how do you know? 10 8 12 6 9 15 Find the corresponding sides and set up an extended proportion. The two triangles are similar by the SSS~ theorem.

Example � Are the two triangles similar, how do you know? 2 Both triangles share angle M, so check the ratios of the sides that include angle M. 8 12 3 The two triangles are Similar by the SAS~ theorem.

Homework � P. 455 #’s 7 -12, 15 -20, 23 -26, 37 -44