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7-3: Identifying Similar Triangles Expectations: G2.3.2: Use theorems about congruent triangles to prove additional theorems and solve problems. G2.3.3: Prove that triangles are similar by SSS, SAS and AA conditions for similarity. 4/29/2017 7-3 Similar Triangles Angle-Angle a. Draw two triangles with angle measures of 75° and 65°. b. Label the 75° angles ∠A and ∠X. c. Label the 65° angles ∠B and ∠Y. 4/29/2017 7-3 Similar Triangles Angle-Angle d. Compare the ratios of corresponding sides. e. What does this tell us about the triangles? 4/29/2017 7-3 Similar Triangles Angle-Angle Triangle Similarity Theorem If two angles of a first triangle are congruent to two angles of a second triangle, then the triangles are similar. 4/29/2017 7-3 Similar Triangles Side-Side-Side a. Draw ∆ABC such that AB = 4, BC = 6 and AC = 7. b. Draw ∆DEF such that DE = 8, EF = 12 and DF = 14. 4/29/2017 7-3 Similar Triangles Side-Side-Side c. Compare corresponding angles. d. What is true about the triangles? 4/29/2017 7-3 Similar Triangles Side-Side-Side Triangle Similarity Theorem If the measures of the corresponding sides of 2 triangles are proportional, then the triangles are similar. 4/29/2017 7-3 Similar Triangles Side-Angle-Side a. Draw ∆KLM such that KL = 4, LM = 5 and m∠L = 60°. b. Draw ∆RST such that RS = 8, ST = 10 and m∠S = 60°. 4/29/2017 7-3 Similar Triangles Side-Angle-Side c. What is true about the triangles? 4/29/2017 7-3 Similar Triangles Sid-Angle-Side Triangle Similarity Theorem If the measures of two sides of one triangle are proportional to two sides of a second triangle and the included angles are congruent, then the triangles are similar. 4/29/2017 7-3 Similar Triangles Equality Properties of Similarity Similarity of figures is reflexive, symmetric and transitive. 4/29/2017 7-3 Similar Triangles Reflexive Property of Similarity F~F 4/29/2017 7-3 Similar Triangles Symmetric Property of Similarity If F ~ G, then G ~ F. 4/29/2017 7-3 Similar Triangles Transitive Property of Similarity If F ~ G and G ~ H, then F ~ H. 4/29/2017 7-3 Similar Triangles Are the following triangles similar? Justify your response. 7.2 12 20 12 9 15 4/29/2017 7-3 Similar Triangles Are the triangles below similar? Justify with a postulate or theorem. 4/29/2017 7-3 Similar Triangles If AB // EF, AD = 9, DB = 16, EC = 2(AE), determine AE, AC, BC and EF C H E A 4/29/2017 F B D 7-3 Similar Triangles Use similar triangles to answer the question below. At 4:00 a yard stick cast a 5 foot shadow. How tall is a tree that has an 18 foot shadow at the same time? 4/29/2017 7-3 Similar Triangles In the figure below, segment AB ⊥ segment DE. The measure of ∠CAD is equal to the measure of ∠CEB. The length of segment CA is 6 units and the length of segment CE is 187 units. If the length of segment AD is 10 units, what is the length of segment EB? B A. 10 B. 20 D C. 25 10 D. 30 C 6 E. 35 18 A E 4/29/2017 7-3 Similar Triangles Solve for x. 4/29/2017 7-3 Similar Triangles Given: LP // MN LJ PJ Prove: LN JM L P J M 4/29/2017 N 7-3 Similar Triangles 4/29/2017 7-3 Similar Triangles Assignment pages 358 – 361, # 13-23 (odds), 27, 37, 39-47 (all). 4/29/2017 7-3 Similar Triangles