Theorem 2-7
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Theorem 2-7
If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent
Given:
<1 and <2 are supplementary; <3 and <4 are supplementary; <2≅<4
Prove:
<1≅<3
2. m<1 + m<2 = 180; m<3+m<4 = 180
Definition of supplementary angles
1. <1 and <2 are supplementary; <3 and <4 are supplementary
Given
4. <2 ≅ <4, or m<2 = m<4
Given
3. m<1 + m<2 = m<3 + m<4
Substitution property
5. m<1 = m<3, or <1 ≅ <3
Subtraction Property of equality
