Question 18 Please

Complete the proof of the following theorem. If two angles are complementary to the same angle, then these angles are congruent. Given: 21 is comp. to 23 42 is comp. to 23 Prove: 41 ~ 42 PROOF Statements Reasons 1. 21 is comp. to 23 1. Question 16 below 42 is comp. to 23 2. mz1 + m43 = 90 2. Question 17 below m42 + m43 = 90 3. mz1 + m23 = mz2 + mz3 3. Question 18 below 4. m41 = m42 4. Question 19 below 5. 41 ~ 42 5. Question 20 below Figure 6: Proof Outline for Questions 16-20 16. Complete Reason 1. (a) Given (b) Definition of complementary angles (c) Transitive Property (d) Vertical angles are congruent (e) None of the above 17. Complete Reason 2. (a) Addition Property of Equality (b) Transitive Property (c) Definition of Supplementary Angles (d) Definition of Complementary Angles (e) None of the above. 7 18. Complete Reason 3. (a) Addition Property of Equality (b) Substitution (c) Angle-Addition Postulate (d) Symmetric Property (e) None of the above. 19. Complete Reason 4. (a) Angle-Addition Postulate (b) Reflexive Property (c) Subtraction Property of Equality (d) Substitution (e) None of the above 20. Complete Reason 5. (a) Proven (b) Angle Congruence Postulate