FAN + MEDAL Diana and Joby wrote the following proofs to prove that vertical angles are congruent. Who is correct? Line segment NT intersects line segment MR forming four angles. Angles 1 and 3 are vertical angles. Angles 2 and 4 are vertical angles. Diana's Proof Statement Justification ∠1 + ∠2 = 180° Definition of Supplementary Angles ∠1 + ∠4 = 180° Definition of Supplementary Angles ∠1 + ∠2 = ∠1 + ∠4 Transitive Property of Equality
Joby's Proof Statement Justification ∠2 = ∠4 Vertical angles are congruent. ∠1 = ∠3 Vertical angles are congruent. Vertical Angles are congruent. Vertical Angle Theorem
Neither Diana nor Joby is correct. Diana doesn't show how the angles are congruent to each other so her proof is wrong. What Joby did is a classical fallacy: assuming your conclusion. So neither of them are correct.
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