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) △cab≅△

Explanation:

Step1: Identify corresponding angles

By the marking of congruent - parts, angles with the same number of arcs are corresponding. So, $\angle A\cong\angle Y$, $\angle B\cong\angle X$, $\angle C\cong\angle Z$.

Step2: Identify corresponding sides

Sides with the same number of tick - marks are corresponding. So, $\overline{AB}\cong\overline{YX}$, $\overline{AC}\cong\overline{YZ}$, $\overline{BC}\cong\overline{ZX}$.

Step3: Write the triangle congruence statement

The order of vertices in the congruence statement should match the corresponding vertices. So, $\triangle CAB\cong\triangle ZYX$.

Answer:

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