Question

given
∠1 and ∠2 are supplementary
∠3 and ∠2 are supplementary
∠4 ≅ ∠3
prove
∠1 ≅ ∠4
statement

1. ∠1 and ∠2 are supplementary
2. ∠3 and ∠2 are supplementary
3. ∠1 ≅ ∠3
4. ∠4 ≅ ∠3
5. ∠1 ≅ ∠4

reason

1. given
2. given
3. ?
4. given
5. transitive property

what geometric reason justifies the transition from statement 1 and 2 to statement 3?
congruent right angles theorem
transitive property
vertical angles theorem
congruent supplements theorem

Explanation:

The Congruent Supplements Theorem states that if two angles are supplementary to the same angle (or to congruent angles), then the two angles are congruent. Here, ∠1 and ∠3 are both supplementary to ∠2. So, by the Congruent Supplements Theorem, ∠1 ≅ ∠3.

Answer:

Congruent Supplements Theorem