Name Class Reteaching 5-4 Date Inverses, Contrapositives, and Indirect Reasoning OBJECTIVE: Writing convincing arguments using indirect reasoning MATERIALS: None Example A Given: ⬔A and ⬔B are not complementary. Prove: ⬔C is not a right angle. Step 1: Assume that ⬔C is a right angle. C Step 2: If ⬔C is a right angle, then by the Triangle Angle-Sum Theorem m⬔A + m⬔B + 90 = 180. So m⬔A + m⬔B = 90. Therefore, ⬔A and ⬔B are complementary. But ⬔A and ⬔B are not complementary. B Step 3: Therefore, ⬔C is not a right angle. Exercises Complete the proofs. 1. Arrange the statements given at the right to complete the steps of the indirect proof. Y Given: XY ⬵ YZ © Pearson Education, Inc. All rights reserved. Prove: ⬔1 ⬵ ⬔4 Step 1: 9 A. But XY ⬵ YZ. Step 2: 9 B. Assume ⬔1 ⬵ ⬔4. Step 3: 9 C. Therefore, ⬔1 ⬵ ⬔4. Step 4: 9 D. ⬔1and ⬔2 are supplementary, and ⬔3 and ⬔4 are supplementary. Step 5: 9 Step 6: 9 1 2 X 3 4 Z E. According to the Converse of the Isosceles Triangle Theorem, XY = YZ or XY ⬵ YZ. F. If ⬔1 ⬵ ⬔4, then by the Congruent Supplements Theorem, ⬔2 ⬵ ⬔3. E 2. Complete the steps below to write a convincing argument using indirect reasoning. Given: 䉭DEF with ⬔D ⬵ ⬔F Prove: EF ⬵ DE Step 1: 9 Step 2: 9 Step 3: 9 D F Step 4: 9 Geometry Chapter 5 Lesson 5-4 Reteaching 9