Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name Class 2-6 Date Practice (continued) Form G Proving Angles Congruent 11. Given: /5 > /2 Prove: /8 > /4 1 2 4 3 Statements 6 5 8 7 1) 9 l5 O l2 Reasons 1) Given 2) /2 > /4 2) 9 Vertical Angles are O. 3) 9 l5 O l4 3) Transitive Property of Congruence 4) 9 l8 O l5 4) Vertical Angles are >. 5) /8 > /4 5) 9 Transitive Property of Congruence 12. Complete the paragraph proof below. A Given: /1 and /2 are complementary D /2 and /3 are complementary BD bisects /ABC 2 1 Prove: m/1 5 45 B 3 We know that and are complementary and /2 and /3 are complementary because these facts are given. By the , . Using m/2 1 m/3 5 90. Given that BD bisects /ABC, it follows that substitution, , or 2(m/3) 5 90. Using the , m/3 5 45. By the Congruent Complements Theorem, . It follows that , because congruent angles have the same measure and by substitution. l1; l2; definition of complementary angles; ml2 5 ml3; ml3 1 ml3 5 90; Division Property of Equality; l1 O l3; ml1 5 ml3; ml1 5 45 13. Writing Look back at the proof in Exercise 11. Rewrite the proof as a paragraph proof. Answers may vary. Sample: It is given that l5 O l2. Since vertical angles are O , it follows that l2 O l4. Using the Transitive Property of Congruence, it follows that l5 O l4. Again, because vertical angles are O , it follows that l8 O l5. Finally, it follows that l8 O l4, using the Transitive Property of Congruence. Prentice Hall Gold Geometry • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 54 C