Question

given
\\( \angle x \\) and \\( \angle y \\) are supplementary
\\( \angle z \\) and \\( \angle y \\) are supplementary
\\( \angle w \cong \angle x \\)
\\( \angle t \cong \angle z \\)
prove
\\( \angle w \cong \angle t \\)

what geometric reason justifies the transition from
statement 1 and 2 to statement 3?

transitive property

congruent right angles theorem

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, ∠X and ∠Z are both supplementary to ∠Y, so by the Congruent Supplements Theorem, ∠X ≅ ∠Z.

Answer:

Congruent Supplements Theorem