Proof Companion
Random proof
Theorems
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Given:
△ABC and DE ǁ AB
Prove:
∠A + ∠ACB + ∠B = 180
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∠DCB + ∠BCE = 180
∠A = ∠ACD and ∠B = ∠BCE
Substitution
Parallel lines form equal alternate interior angles
Angle addition theorem
Substitution
∠A + ∠ACB + ∠B = 180
∠ACD + ∠ACB + ∠BCE = 180
Statements
△ABC and DE ǁ AB
∠ACD + ∠ACB = ∠DCB
Reasons
Given
The angles in a linear pair are supplementary