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LESSON 4.6 NAME _________________________________________________________ DATE ___________ Challenge: Skills and Applications For use with pages 236–242 1. In the diagram, AC BC, BD CD, and C CA bisects BCD. a. Find mB. b. Write a paragraph proof for your result. c. Prove that AC AD. B D A Lesson 4.6 2. Write a two-column proof. H Given: EF FH HG, FG GI Prove: EG HI F 2 3 4 1 G I E 3. A segment which extends from a vertex of a triangle to the L side opposite the vertex is called an altitude if it is perpendicular to that side. In this exercise, you will prove that if two altitudes of a triangle are congruent, then the triangle is isosceles. Write a paragraph proof. M N O Given: KM JL, JN LK, KM JN Prove: JL KL J K 4. Write a two-column proof of the Base Angles Theorem B without drawing any additional segments or points. Given: ABC, AB AC Prove: B C A C 5. In this exercise, you will prove the HL Congruence Theorem. R U Q S T Write a paragraph proof (without using the HL Congruence Theorem). Given: PQR and STU, QR TU, PR SU, PQR and STU are right angles. Prove: PQR STU P V (Hint: Extend ST to V so that PQ TV. Draw UV. Prove that PQR VTU and VTU STU. Copyright © McDougal Littell Inc. All rights reserved. Geometry Chapter 4 Resource Book 93