Congruent Supplements Theorem

Consider two pairs of supplementary angles: ∠ 1 and ∠ 2, and ∠ 3 and ∠ 2. By the definition of supplementary angles, the sum of the angle measures in each of these pairs is 180^(∘). m∠ 1+m∠ 2=180^(∘) m∠ 3+m∠ 2=180^(∘) The right-hand sides of the equations are the same. Therefore, by the Transitive Property of Equality the left-hand sides must also be equal. m∠ 1+m∠ 2= 180^(∘) m∠ 3+m∠ 2= 180^(∘) ⇓ m∠ 1+m∠ 2= m∠ 3+m∠ 2 Finally, by using the Subtraction Property of Equality m∠ 2 can be subtracted from each side of the obtained equation. m∠ 1+m∠ 2=m∠ 3+m∠ 2 ⇕ m∠ 1=m∠ 3 The measures of ∠ 1 and ∠ 3 are the same, which indicates that these angles are congruent.