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) (overline{ab}congoverline{}) ∠b≅∠ (overline{ac}congoverline{}) ∠c≅∠ (overline{bc}congoverline{}) (c) △cba≅△

Explanation:

Step1: Identify corresponding angles

By the property of congruent triangles, angles with same markings are congruent. So, $\angle A\cong\angle Z$, $\angle B\cong\angle X$, $\angle C\cong\angle Y$.

Step2: Identify corresponding sides

Sides with same number of markings are congruent. So, $\overline{AB}\cong\overline{ZX}$, $\overline{AC}\cong\overline{ZY}$, $\overline{BC}\cong\overline{XY}$.

Step3: Write triangle - congruence statement

The order of vertices in congruence statement matters. Since $\angle C\cong\angle Y$, $\angle B\cong\angle X$, $\angle A\cong\angle Z$, we have $\triangle CBA\cong\triangle YXZ$.

Answer:

(a) $\angle A\cong\angle Z$, $\angle B\cong\angle X$, $\angle C\cong\angle Y$
(b) $\overline{AB}\cong\overline{ZX}$, $\overline{AC}\cong\overline{ZY}$, $\overline{BC}\cong\overline{XY}$
(c) $\triangle CBA\cong\triangle YXZ$