Question

given
∠x and ∠y are supplementary
∠z and ∠y are supplementary
∠w ≅ ∠x
∠t ≅ ∠z
prove
∠w ≅ ∠t
statement

1. ∠x and ∠y are supplementary
2. ∠z and ∠y are supplementary
3. ∠x ≅ ∠z
4. ∠w ≅ ∠x
5. ∠t ≅ ∠z
6. ∠w ≅ ∠t

reason

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

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

Explanation:

Step1: Recall Congruent Supplements Theorem

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.
In this case, \(\angle X\) and \(\angle Z\) are both supplementary to \(\angle Y\) (from statement 1 and 2).

Answer:

Congruent Supplements Theorem