Question

(a) complete the congruence statements below.
∠w≅ (choose one)
∠y≅ (choose one)
∠x≅ (choose one)
(b) complete the congruence statements below.
wy≅ (choose one)
yx≅ (choose one)
xw≅ (choose one)
(c) are all three pairs of corresponding angles and all three pairs of corresponding sides congruent?
yes, and the triangles are not congruent.
yes, and the triangles are congruent.
no, and the triangles are not congruent.
no, and the triangles are congruent.

Explanation:

Step1: Identify corresponding angles

When two triangles are congruent, corresponding angles are equal. If we assume $\triangle CDE\cong\triangle XWY$ (by proper orientation - not given explicitly but based on congruence rules), $\angle W$ corresponds to $\angle D$, $\angle Y$ corresponds to $\angle E$, $\angle X$ corresponds to $\angle C$.

Step2: Identify corresponding sides

Corresponding sides of congruent triangles are equal. So, $\overline{WY}$ corresponds to $\overline{DE}$, $\overline{YX}$ corresponds to $\overline{EC}$, $\overline{XW}$ corresponds to $\overline{CD}$.

Step3: Recall congruence definition

Two triangles are congruent if all three pairs of corresponding angles and all three pairs of corresponding sides are congruent.

Answer:

(a) $\angle W\cong\angle D$, $\angle Y\cong\angle E$, $\angle X\cong\angle C$
(b) $\overline{WY}\cong\overline{DE}$, $\overline{YX}\cong\overline{EC}$, $\overline{XW}\cong\overline{CD}$
(c) Yes, and the triangles are congruent.