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November 29, 2012 6-3 Similar Triangles Angle-Angle Similarity: (AA ) *If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. A D B A C = D E and then C ABC F = E DFE 6-3 Similar Triangles Side-Side-Side Similarity (SSS ): *If the measures of the corresponding sides of two triangles are proportional, the the triangles are similar. M L N K J JK MN JKL P KL NP JL MP MNP November 29, 2012 6-3 Similar Triangles Side-Angle-Side Similarity (SAS ): *If the measures of two sides of one triangle are proportional to the corresponding sides of another triangle and the included angles are congruent, the the triangles are similar. T X RT YX RS YZ and Z Y S R R= Y then RST YZX 6-3 Similar Triangles Similarity of triangles is reflexive, symmetric, and transitive: Reflexive: Symmetric: Transitive: November 29, 2012 6-3 Similar Triangles Example 1: In the figure, AB DC. BE = 27, DE = 45, AE = 21, and CE = 35. Determine which triangles in the figure are similar. C B E D A 6-3 Similar Triangles R Example 2: Given RS UT, RS = 4, UT = 10 RQ = x + 3, QT = 2x + 10, find RQ and QT. S Q U T November 29, 2012 Example 3: 6-3 Similar Triangles Josh wanted to measure the height of the Sears Tower in Chicago. He used a 12-foot light pole and measured its shadow at 1 p.m. The length of the light poles shadow was 2 feet. Then he measured the length of the Sears Tower shadow and it was 242 feet at that time. What is the height of the Sears Tower?