lesson 6.2 congruent angles pp. 214-220

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Lesson 6.2 Congruent Angles pp. 214-220

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Lesson 6.2 Congruent Angles pp. 214-220. Objective: To identify, prove, and applytheorems relating to congruent angles. EXAMPLE 1 Prove: All right angles are congruent. Theorem 6.3 Supplements of congruent angles are congruent. EXAMPLE 2 Prove: Theorem 6.3. - PowerPoint PPT Presentation

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Page 1: Lesson 6.2 Congruent Angles pp. 214-220

Lesson 6.2Congruent Angles

pp. 214-220

Lesson 6.2Congruent Angles

pp. 214-220

Page 2: Lesson 6.2 Congruent Angles pp. 214-220

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

Page 3: Lesson 6.2 Congruent Angles pp. 214-220

EXAMPLE 1 Prove: All right angles are congruent.

Page 4: Lesson 6.2 Congruent Angles pp. 214-220

Theorem 6.3Supplements of congruent angles are congruent.

Page 5: Lesson 6.2 Congruent Angles pp. 214-220

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

Page 6: Lesson 6.2 Congruent Angles pp. 214-220

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

Page 7: Lesson 6.2 Congruent Angles pp. 214-220

Theorem 6.4Complements of congruent angles are congruent.

11 223344

exercise 8exercise 8

Page 8: Lesson 6.2 Congruent Angles pp. 214-220

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.

Page 9: Lesson 6.2 Congruent Angles pp. 214-220

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

Page 10: Lesson 6.2 Congruent Angles pp. 214-220

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

Page 11: Lesson 6.2 Congruent Angles pp. 214-220

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

Page 12: Lesson 6.2 Congruent Angles pp. 214-220

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

Page 13: Lesson 6.2 Congruent Angles pp. 214-220

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

Page 14: Lesson 6.2 Congruent Angles pp. 214-220

2. A A

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

2. Def. of ’s

Statements ReasonsStatements Reasons

Page 15: Lesson 6.2 Congruent Angles pp. 214-220

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

Page 16: Lesson 6.2 Congruent Angles pp. 214-220

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

Page 17: Lesson 6.2 Congruent Angles pp. 214-220

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

exercise 17exercise 17

Page 18: Lesson 6.2 Congruent Angles pp. 214-220

Homeworkpp. 218-220Homeworkpp. 218-220

Page 19: Lesson 6.2 Congruent Angles pp. 214-220

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

Page 20: Lesson 6.2 Congruent Angles pp. 214-220

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

(Theorem 4.1)

Page 21: Lesson 6.2 Congruent Angles pp. 214-220

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

is the other. (Theorem 4.3)

Page 22: Lesson 6.2 Congruent Angles pp. 214-220

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

a linear pair. (Theorem 4.4)

Page 23: Lesson 6.2 Congruent Angles pp. 214-220

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

4.5)

Page 24: Lesson 6.2 Congruent Angles pp. 214-220

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

right angles. (Theorem 4.6)