Question

given
∠1≅∠2
prove
∠3≅∠4
statement reason

1. ∠1≅∠2 1) given
2. ∠2≅∠4 2) vertical angles theorem
3. ∠1≅∠4 3) transitive property
4. ∠1≅∠3 4) ?
5. ∠3≅∠4 5) transitive property

what geometric reason justifies the transition from statement 3 to statement 4?
congruent supplements theorem
vertical angles theorem
congruent right angles theorem
reflexive property

Explanation:

The Congruent Supplements Theorem states that if two angles are supplementary to the same angle (or to congruent angles), then they are congruent. In this case, ∠1 and ∠3 are supplementary to ∠2 and ∠4 respectively. Since ∠1 ≅ ∠2 (given) and ∠2 ≅ ∠4 (Vertical Angles Theorem), by the Congruent Supplements Theorem, ∠1 ≅ ∠3.

Answer:

Congruent Supplements Theorem