Question

ab is parallel to de. alicia noticed that: • ∠w≅∠x • ∠y≅∠x note: alicia used the following theorems: • when a transversal crosses parallel lines, alternate interior angles are congruent. • vertical angles are congruent. what theorem can alicia prove using these congruent angles? choose 1 answer: a when a transversal crosses parallel lines, alternate exterior angles are supplementary. b angles that form a linear pair are complementary. c when a transversal crosses parallel lines, same - side interior angles are congruent. d when a transversal crosses parallel lines, corresponding angles are congruent.

Explanation:

Given $\angle w\cong\angle x$ (by alternate - interior angles theorem as $AB\parallel DE$) and $\angle y\cong\angle x$ (by vertical - angles theorem). Since $\angle w$ and $\angle y$ are corresponding angles with respect to the parallel lines $AB$ and $DE$ and the transversal, and $\angle w\cong\angle y$ (by the transitive property of congruence as $\angle w\cong\angle x$ and $\angle y\cong\angle x$), this shows that when a transversal crosses parallel lines, corresponding angles are congruent.

Answer:

D. When a transversal crosses parallel lines, corresponding angles are congruent.