Properties of Angle Congruence relationships
Theorem |
Theorem : Properties of Angle Congruence
Angle congruence is reflexive, symmetric, and transitive.
Here are some examples: |
REFLEXIVE |
For any angle A,< A @ < A |
SYMMETRIC |
If< A < B, then< B < A. |
TRANSITIVE |
If< A < B , and< B < C , then< A < C |
Example : Transitive Property of Angle Congruence
Prove the Transitive Property of Congruence for angles.
Solution: To prove the Transitive Property of Congruence for angles, begin by drawing three congruent angles.
Label the vertices as A, B , and C .
Given :< A< B,
< B < C
Prove:< A < C
Statements |
Reasons |
1.< A < B
< B < C |
1. Given |
2. m< A = m< B |
2. Definition of congruent angle |
3. m< B = m< C |
3. Definition of congruent angle |
4. m< A = m< C |
4. Transitive property of equality |
5.< A < C |
5. Definition of congruent angles |
|
