lesson 6.2 congruent angles pp. 214-220

Lesson 6.2Congruent Angles

pp. 214-220

Lesson 6.2Congruent Angles

pp. 214-220

Objective:To identify, prove, and applytheorems relating to congruent angles.

EXAMPLE 1 Prove: All right angles are congruent.

Theorem 6.3Supplements of congruent angles are congruent.

EXAMPLE 2 Prove: Theorem 6.3EXAMPLE 2 Prove: Theorem 6.3

EXAMPLE 3 Prove: If mAXB = mDXY, then mAXD = mBXY

Theorem 6.4Complements of congruent angles are congruent.

11 223344

exercise 8exercise 8

Theorem 6.5Angle congruence is an equivalence relation.

Reflexive: A ASymmetric: If A B, then B A.Transitive: If A B and B C, then A C.

10. Transitive prop. of congruent ’sGiven: A B and B CProve: A C

2. mA = mBmB = mC

4. A C

1. A B B C

1. Given

2. Def. of ’s

3. mA = mC 3. Trans. prop. of equality

4. Def. of ’s

Statements ReasonsStatements Reasons

12. Symmetric prop. of cong. ’sGiven: A BProve: B A

2. mA = mB

4. B A

1. A B 1. Given2. Def. of ’s

3. mB = mA 3. Symm. prop. of equality

4. Def. of ’s

Statements ReasonsStatements Reasons

13. Reflexive prop. of cong. ’sGiven: mA = mAProve: A A

2. A A

1. mA = mA 1. Reflex. prop. of equality

2. Def. of ’s

Statements ReasonsStatements Reasons

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

exercise 15exercise 15

Theorem 6.7Adjacent 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 16exercise 16

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

exercise 17exercise 17

Homeworkpp. 218-220Homeworkpp. 218-220

Reasons for 1-6, p. 218.1. Given2. Def. of cong. ’s3. Vertical Angle Theorem 4. Def. of cong. ’s5. Substitution 6. Def. of cong. ’s

■ Cumulative ReviewDiagram each theorem listed below.21. All right angles are congruent.

(Theorem 4.1)

■ Cumulative ReviewDiagram each theorem listed below.22. If one angle of a linear pair is right, so

is the other. (Theorem 4.3)

■ Cumulative ReviewDiagram each theorem listed below.23. Adjacent supplementary angles form

a linear pair. (Theorem 4.4)

■ Cumulative ReviewDiagram each theorem listed below.24. Vertical Angle Theorem. (Theorem

4.5)

■ Cumulative ReviewDiagram each theorem listed below.25. Congruent supplementary angles are

right angles. (Theorem 4.6)