We'll say that ∠1 and ∠2 are both supplementary to ∠3. Our goal is to prove that ∠1 and ∠2 are congruent. Supplementary angles are just like complementary angles, except their sum is 90°, not 180°. That means m∠1 + m∠3 = 180 and m∠2 + m∠3 = 180. Subtracting m∠3 from both sides of both equations we have both m∠1 and m∠2 equaling 180 – m∠3. If that's not congruent, we don't know what is. Statements  Reasons  1. ∠1 and ∠3 are supplementary  Given  2. ∠2 and ∠3 are supplementary  Given  3. m∠1 + m∠3 = 180  Definition of supplementary  4. m∠2 + m∠3 = 180  Definition of supplementary  5. m∠1 = 180 – m∠3  Subtract m∠3 from (3)  6. m∠2 = 180 – m∠3  Subtract m∠3 from (4)  7. m∠1 = m∠2  Transitive property of equality (5 and 6)  8. ∠1 ≅ ∠2  Definition of congruence (7) 
