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

Question

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

anonymous · Answer

Joby's Proof

Statement	Justification
∠2 = ∠4	Vertical angles are congruent.
∠1 = ∠3	Vertical angles are congruent.
Vertical Angles are congruent.	Vertical Angle Theorem

hannahc234 · Answer

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.