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Working with Similar Triangles 1. Use the AA similarity postulate, the SAS similarity theorem, and the SSS similarity theorem to prove triangles similar. 2. Use similar triangles to deduce information about segments or angles. 3. Apply the Triangle Proportionality Theorem and its corollary 4. State and apply the Triangle Angle-Bisector Theorem 7-4 A postulate for Similar Triangles AA Similarity Postulate – If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Examples: the key to proving two triangles similar is to first show two pairs of congruent angles D A 1.) Given: AC // BD Prove: ▲AOC ~ Statements 1. AC // BD O ▲BOD Reasons 1. Given 2. <A < B; <C <D 2. alt int <’s congruent 3. ▲AOC ~ ▲BOD 3. AA ~ postulate B C R 2.) Given: AB BF RH AF <1 <2 Prove: HRBF = BAHA Statements 1. AB BF; RH AF <1 <2 2. <RHA <FBA 3. ▲RHA ~ ▲ABF 4. HA HR BF BA 5. HR BF = BA HA 1 Reasons 1. Given A F 2 2. all right angles are congruent 3. AA ~ postulate 4. Corr. Sides of ~ triangles are prop. 5. Means-ext prop (cross mult) H B Tell whether or not there are two similar triangles shown. 1.) 2.) 68˚ 68˚ 80˚ 80˚ 3.) 4.) 70˚ 70˚ Find the value of x 5.) 6.) x 8 5 3 y 1 3 x 3 4