Postulate & Theorems for Similar Triangles Unit 6: Lesson

Postulate 15 AA Similarity Postulate : If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar Example 1: Tell whether the triangles are similar or not similar a.b. c.d. Practice p257 written exercises #1-9 odd Similar

Example 2: Find the value of x a. b. △ ABC ∼ ______ c.y = ______ d. Practice p257 written exercises 10 and x 3 C B E A D y x X = 5/3 32/7 9/4 △ EBD

Theorem 7-1 SAS Similarity Thm : If an angle of one triangle is congruent to the angle of another triangle and the sides including those angles are in proportion, then the triangles are similar Theorem 7-2 SSS Similarity Thm: If the sides of two triangles are in proportion, then the triangles are similar Example 3: Name similar triangles and give the postulate or theorem that justifies your answer. a. b.c. A BC D A E K C B L E D N M O 80 ° △ ADE ∼△ ABC AA ∼ Post. △ CDE ∼△ CAB SAS ∼ Thm △ KLM ∼△ KON SSS ∼ Thm

Practice p264 Classroom Exercises #1-4 Example 4: If △ ABC ∼△ DEF, does correspond to ? Does correspond to ? Practice 1.The measures of the sides of △ ABC are 4, 5, and 7, and the measures of the sides of △ XYZ are 16, 20, and 28. Are the two triangles similar? 1.In △ ABC, AB = 2, AC = 5, and BC = 6. In △ XYZ, XY = 2.5, YZ = 2, and XZ = 3. Is △ ABC ∼ △ XYZ ? Homework: Practice Worksheet 7.4 and 7.5 Yes No