Question

the triangles below are congruent and their corresponding parts are name all the corresponding congruent angles and sides. then, complete the triangle congruence statement. (a) $\angle a \cong \angle \square$ $\angle b \cong \angle \square$ $\angle c \cong \angle \square$ (b) $\overline{ab} \cong \overline{\square}$ $\overline{ac} \cong \overline{\square}$ $\overline{bc} \cong \overline{\square}$ (c) $\triangle bac \cong \triangle \square$

Explanation:

Step1: Identify corresponding angles

In congruent triangles, corresponding angles are marked with the same number of arcs. So, $\angle A$ (one arc) corresponds to $\angle Z$ (one arc), $\angle B$ (two arcs) corresponds to $\angle X$ (two arcs), and $\angle C$ (one arc) corresponds to $\angle Y$ (one arc). Thus, $\angle A \cong \angle Z$, $\angle B \cong \angle X$, $\angle C \cong \angle Y$.

Step2: Identify corresponding sides

Corresponding sides have the same number of tick marks. $\overline{AB}$ (one tick) corresponds to $\overline{ZX}$ (one tick), $\overline{AC}$ (two ticks) corresponds to $\overline{ZY}$ (two ticks), and $\overline{BC}$ (one tick) corresponds to $\overline{XY}$ (one tick). So, $\overline{AB} \cong \overline{ZX}$, $\overline{AC} \cong \overline{ZY}$, $\overline{BC} \cong \overline{XY}$.

Step3: Triangle congruence statement

The order of vertices in the congruence statement should match the corresponding vertices. From angles and sides, $B$ corresponds to $X$, $A$ corresponds to $Z$, $C$ corresponds to $Y$. So, $\triangle BAC \cong \triangle XZY$.

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) $\triangle BAC \cong \triangle XZY$