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) $\angle a \cong \angle \square$ $\angle b \cong \angle \square$ $\angle c \cong \angle \square$ (b) $\overline{ab} \cong \overline{\square}$ $\overline{ac} \cong \overline{\square}$ $\overline{bc} \cong \overline{\square}$ (c) $\triangle bca \cong \triangle \square$

Explanation:

Match marked congruent parts:

1. Angles: $\angle A$ (double arc) matches $\angle Z$ (double arc); $\angle B$ (single arc) matches $\angle X$ (single arc); $\angle C$ matches the unmarked $\angle Y$.
2. Sides: $\overline{AB}$ (single tick) matches $\overline{ZX}$ (single tick); $\overline{AC}$ (double tick) matches $\overline{ZY}$ (double tick); $\overline{BC}$ (single hash) matches $\overline{XY}$ (single hash).
3. Triangle congruence: Map vertices from $\triangle BCA$ to their matches: $B\to X$, $C\to Y$, $A\to Z$.

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)
$\triangle BCA \cong \triangle XYZ$