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)