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Geometry Notes 6.4 and 6.5 Name_________________________ Proving Triangles Similar by AA, SSS, and SAS Postulate 22: Angle-Angle (AA) Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. K Y L Z X J Theorem 6.2: Side-Side-Side (SSS) Similarity Theorem If the corresponding side lengths of two triangles are proportional, then the triangles are similar. R A S B Example: Is either or B similar to 12 D 8 ? H F 10 12 6 C 8 9 E A 16 C J Example: Find the value of x that makes 3( x 1) G 16 . T Theorem 6.3: Side-Angle-Side (SAS) Similarity Theorem If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar. X M P N Y Z Examples 1. Determine whether the triangles are similar. If they are, write a similarity statement. D H C 26 64 E K G Show that the two triangles are similar. Then write a similarity statement. 2. ABE and ACD 3. CDF and DEF D A E 52 B D 58 32 52 C C F E 4. A flagpole casts a shadow that is 50 feet long. At the same time, a woman standing nearby who is five feet four inches tall casts a shadow that is 40 inches long. How tall is the flagpole to the nearest foot? 5. Tell what method you would use to show that the triangles are similar. D A 15 18 C B 9 30 E Example: Determine if the triangles are similar. If they are, write a similarity statement and justify why they are similar.