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Given: angle 1 is supplementary to angle 2 and angle 1 is congruent to angle 3.

Prove: angle 3 is supplementary to angle 2.

Given angle 1 is supplementary to angle 2 and angle 1 is congruent to angle 3 Prove angle 3 is supplementary to angle 2 class=

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 ∠1 and ∠2 are supplementary    // given∠3 and ∠4 are supplementary    // given∠1 ≅ ∠3    // given m∠1 + m∠2 = 180°    // definition of supplementary anglesm∠3 + m∠4 = 180°    // definition of supplementary angles m∠1 + m∠2 = m∠3 + m∠4    // transitive property of equality m∠1 = m∠3    // definition of congruent angles m∠1 + m∠2 = m∠1 + m∠4    // substitution property of equality (replaced m∠3 with m∠1) m∠2 = m∠4    // subtraction property of equality (subtracted m∠1 from both sides) ∠2 ≅ ∠4    // definition of congruent angles


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