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Unit 3: Triangles Day 14 Notes Proving Triangles Similar (PH 8-3) Review: a. Name: ___________________________ Date: _________________ Hour: ____ Name the postulate or theorem you can use to prove the triangles congruent. b. c. Patterns can also be used to show that two triangles are similar to each other. Postulate 8-1: Angle-Angle Similarity (AA ~) Postulate If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. TRS ~ PLM Example 1: ̅̅̅̅̅ ̅̅̅̅. Explain why the triangles are similar. Write a similarity statement. __________ ~ __________ Theorem 8-1: 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. Theorem 8-2: Side-Side-Side Similarity (SSS ~) Theorem If the corresponding sides of two triangles are proportional, then the triangles are similar. Example 2: Explain why the triangles must be similar. a. b. c. Similar triangles are useful for measuring something that is difficult to obtain directly. This is called an indirect measurement. Example 3: Joan places a mirror 24 ft from the base of a tree. When she stands 3 ft from the mirror, she can see the top of the tree reflected in it. If her eyes are 5 ft above the ground, how tall is the tree? Homework: Day 14 Worksheet