Question

the triangles below are congruent and their corresponding parts are marked. name all the corresponding congruent angles and sides. then, complete the triangle congruence statement. (a) ∠a≅∠□ ∠b≅∠□ ∠c≅∠□ (b) $overline{ab}congoverline{□}$ $overline{ac}congoverline{□}$ $overline{bc}congoverline{□}$ (c) △cab≅△□

Explanation:

Step1: Identify corresponding angles

Congruent triangles have matching angles. By comparing the marked parts, $\angle A$ corresponds to $\angle Y$, $\angle B$ corresponds to $\angle Z$, $\angle C$ corresponds to $\angle X$.

Step2: Identify corresponding sides

Corresponding sides of congruent triangles match. So, $\overline{AB}\cong\overline{YZ}$, $\overline{AC}\cong\overline{YX}$, $\overline{BC}\cong\overline{ZX}$.

Step3: Write triangle - congruence statement

The order of vertices in the congruence statement matters. Since $\angle C$ corresponds to $\angle X$, $\angle A$ corresponds to $\angle Y$, and $\angle B$ corresponds to $\angle Z$, we have $\triangle CAB\cong\triangle XYZ$.

Answer:

(a) $\angle A\cong\angle Y$, $\angle B\cong\angle Z$, $\angle C\cong\angle X$
(b) $\overline{AB}\cong\overline{YZ}$, $\overline{AC}\cong\overline{YX}$, $\overline{BC}\cong\overline{ZX}$
(c) $\triangle CAB\cong\triangle XYZ$