Complete the paragraph proof.
Given: ∠1 and ∠2 are supplementary, and ∠2 and ∠3 are supplementary.
Prove: ∠1 ≅ ∠3
Angle 1 is acute, angle 2 is obtuse, and angle three is acute.
By definition of supplementary angles, m∠1 + m∠2 = _____ (a) and m∠2 + m∠3 = _____ (b). Then, m∠1 + m∠2 = m∠2 + m∠3 by the __________ (c). Subtract m∠2 from each side. You get m∠1 = ______ (d), or ∠1 ≅ _____ (e).
(5 points)
By definition of supplementary angles, m∠1 + m∠2 = 180° (a) and m∠2 + m∠3 = 180° (b).
Then, m∠1 + m∠2 = m∠2 + m∠3 by the Transitive Property of Equality (c).
Subtracting m∠2 from each side gives us m∠1 = m∠3 (d), or ∠1 ≅ ∠3 (e).