Theorem 2-7

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