Triangle Similarity Advanced Geometry Similarity Lesson 3

In the Triangle Congruence unit we talked about four tests for proving that two triangles are congruent; SSS Congruence, SAS Congruence, ASA Congruence, and AAS Congruence. There are also tests to prove that two TRIANGLES are similar: SAS Similarity AA Similarity, SSS Similarity, and

Two pairs of corresponding angles are CONGRUENT. AA Similarity

Three pairs of corresponding sides are PROPORTIONAL. SSS Similarity

Two pairs of corresponding sides are PROPORTIONAL SAS Similarity the included angles are CONGRUENT. and

EXAMPLES: Determine whether each pair of triangles is similar. Justify your answer. Yes; AA Similarity No; Correpsonding sides are not proportional. No; There is not enough information.

EXAMPLE: Given RS = 4, RQ = x + 3, QT = 2x + 10, and UT = 10. Find RQ and QT.

EXAMPLE: 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 shadow was 2 feet. Then he measured the length of Sears Tower’s shadow and it was 242 feet at the same time. What is the height of the Sears Tower?

EXAMPLE: Triangles KLJ and MNJ have vertices Justify that

EXAMPLE: Simplify