Question

iana 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 Substitution 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
Diana is correct, but Joby is not.
Both Diana and Joby are correct.
Neither Diana nor Joby is correct.
Joby is correct, but Diana is not.

Answer 1

Both Diana and Joby are correct.