Question

given that ∠x≅∠d, and de≅xw, what is the third congruence needed to prove that △xwy≅△dec by asa?
a. ∠y≅∠c
b. ∠y≅∠e
c. ∠w≅∠c
d. ∠w≅∠e

Explanation:

Step1: Recall ASA congruence criterion

ASA (Angle - Side - Angle) requires two pairs of congruent angles and the included side congruent. We already have $\angle X\cong\angle D$ (given) and $DE\cong XW$ (given). We need the angles adjacent to the given side to be congruent.

Step2: Identify the required angle

The angle adjacent to $XW$ in $\triangle XWY$ is $\angle W$ and the angle adjacent to $DE$ in $\triangle DEC$ is $\angle E$. So we need $\angle W\cong\angle E$.

Answer:

D. $\angle W\cong\angle E$