Date: Topic: Proving Triangles Similar (7.6) Warm-up: Find the similarity ratio, x, and y. The triangles are similar. 6 7 The similarity ratio is: Find x: y x 12 Find y: 6 6 (Round answers to the nearest tenth) 11.7

Side Side Side Similarity Theorem (SSS~) If all of the corresponding sides of two triangles have the same proportion to one another, then the triangles are similar. S: by SSS~, The proportions are equal:

S: The proportions are equal The proportions are not equal Use SSS~ to determine which pair of triangles are similar. by SSS~

Side Angle Side Similarity Theorem (SAS~) If one angle of a triangle is congruent to an angle of a second triangle, and the sides including the two angles have the same proportion to one another, then the triangles are similar. S: A: S: by SAS~, The proportions are equal Included angles are congruent

S: A: S: A: S: The proportions are equal Use SAS~ to determine which pair of triangles are similar. The proportions are equal Included angles are congruent by SAS~

Angle Angle Similarity Theorem (AA~) If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. A: By AA~, Two angles are congruent:

-136° Use AA~ to determine which pair of triangles are similar. -96° -155° A: by AA~ Two angles are congruent: Two angles are not congruent: