Q:

Amanda and Stephen 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. Amanda's Proof Statement Justification ∠1 + ∠4 = 180° Definition of Supplementary Angles ∠3 + ∠4 = 180° Definition of Supplementary Angles ∠1 + ∠4 = ∠3 + ∠4 Transitive Property of Equality ∠1 ≅ ∠3 Subtraction Property of Equality Stephen's Proof Statement Justification ∠1 + ∠2 = 180° Definition of Supplementary Angles ∠2 + ∠3 = 180° Definition of Supplementary Angles ∠1 + ∠2 = ∠2 + ∠3 Transitive Property of Equality ∠1 ≅ ∠3 Subtraction Property of Equality

Accepted Solution

A:
In fact, both Amanda's and Stephen's profs are correct; they are just using different supplementary angles. Amanda's is using the supplementary angles ∠1 and ∠4, and ∠3 and ∠4, whereas Stephen is using ∠1 and ∠2, and ∠2 and ∠3.  Please check the picture to visualize this more effectively.