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7-3: Identifying Similar Triangles

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. Angle-Angle.

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7-3: Identifying Similar Triangles

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  1. 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. 7-3 Similar Triangles

  2. 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. 7-3 Similar Triangles

  3. Angle-Angle • d. Compare the ratios of corresponding sides. e. What does this tell us about the triangles? 7-3 Similar Triangles

  4. 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. 7-3 Similar Triangles

  5. 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. 7-3 Similar Triangles

  6. Side-Side-Side • c. Compare corresponding angles. d. What is true about the triangles? 7-3 Similar Triangles

  7. Side-Side-Side Triangle Similarity Theorem • If the measures of the corresponding sides of 2 triangles are proportional, then the triangles are similar. 7-3 Similar Triangles

  8. 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°. 7-3 Similar Triangles

  9. Side-Angle-Side • c. What is true about the triangles? 7-3 Similar Triangles

  10. 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. 7-3 Similar Triangles

  11. Equality Properties of Similarity • Similarity of figures is reflexive, symmetric and transitive. 7-3 Similar Triangles

  12. Reflexive Property of Similarity • F ~ F 7-3 Similar Triangles

  13. Symmetric Property of Similarity • If F ~ G, then G ~ F. 7-3 Similar Triangles

  14. Transitive Property of Similarity • If F ~ G and G ~ H, then F ~ H. 7-3 Similar Triangles

  15. Are the following triangles similar? Justify your response. 7.2 12 12 20 9 15 7-3 Similar Triangles

  16. Are the triangles below similar? Justify with a postulate or theorem. 7-3 Similar Triangles

  17. If AB // EF, AD = 9, DB = 16, EC = 2(AE), determine AE, AC, BC and EF C H E F A B D 7-3 Similar Triangles

  18. 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? 7-3 Similar Triangles

  19. 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? • 10 • 20 • 25 • 30 • 35 B D 10 C 6 18 A E 7-3 Similar Triangles

  20. Solve for x. 7-3 Similar Triangles

  21. Given: LP // MN L P J M N 7-3 Similar Triangles

  22. 7-3 Similar Triangles

  23. Assignment • pages 358 – 361, • # 13-23 (odds), 27, 37, 39-47 (all). 7-3 Similar Triangles

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