Lesson 6.2 Congruent Angles pp. 214-220

1. Lesson 6.2 Congruent Angles pp. 214-220

2. Objective: To identify, prove, and apply theorems relating to congruent angles.

3. EXAMPLE 1Prove:All right angles are congruent.

4. Theorem 6.3 Supplements of congruent angles are congruent.

5. EXAMPLE 2Prove:Theorem 6.3

6. EXAMPLE 3Prove:If mAXB = mDXY, then mAXD = mBXY

7. 4 3 1 2 Theorem 6.4 Complements of congruent angles are congruent. exercise 8

8. Theorem 6.5 Angle congruence is an equivalence relation. Reflexive: A  A Symmetric: If A  B, then B  A. Transitive: If A  B and B  C, then A  C.

9. 10. Transitive prop. of congruent ’s Given: A  B and B  C Prove: A  C

10. Statements Reasons 1. A  B B  C 1. Given 2. mA = mB mB = mC 2. Def. of  ’s 3. mA = mC 3. Trans. prop. of equality 4. A  C 4. Def. of  ’s

11. 12. Symmetric prop. of cong. ’s Given: A  B Prove: B  A

12. Statements Reasons 1. A  B 1. Given 2. mA = mB 2. Def. of  ’s 3. mB = mA 3. Symm. prop. of equality 4. B  A 4. Def. of  ’s

13. 13. Reflexive prop. of cong. ’s Given:mA = mA Prove: A  A

14. Statements Reasons 1. mA = mA 1. Reflex. prop. of equality 2. A  A 2. Def. of  ’s

15. Theorem 6.6 Adjacent Angle Sum Theorem. If two adjacent angles are congruent to another pair of adjacent angles, then the larger angles formed are congruent. exercise 15

16. Theorem 6.7 Adjacent Angle Portion Theorem. If two angles, one in each of two pairs of adjacent angles, are congruent, and the larger angles formed are also congruent, then the other angles are congruent. exercise 16

17. Theorem 6.8 Congruent Angle bisector Theorem. If two congruent angles are bisected, then the four resulting angles are congruent. exercise 17

18. Homework pp. 218-220

19. Reasons for 1-6, p. 218. 1. Given 2. Def. of cong. ’s 3. Vertical Angle Theorem 4. Def. of cong. ’s 5. Substitution 6. Def. of cong. ’s

20. ■ Cumulative Review Diagram each theorem listed below. 21. All right angles are congruent. (Theorem 4.1)

21. ■ Cumulative Review Diagram each theorem listed below. 22. If one angle of a linear pair is right, so is the other. (Theorem 4.3)

22. ■ Cumulative Review Diagram each theorem listed below. 23. Adjacent supplementary angles form a linear pair. (Theorem 4.4)

23. ■ Cumulative Review Diagram each theorem listed below. 24. Vertical Angle Theorem. (Theorem 4.5)

24. ■ Cumulative Review Diagram each theorem listed below. 25. Congruent supplementary angles are right angles. (Theorem 4.6)