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

Explanation:

Step1: Analyze congruent angles

In congruent triangles, corresponding angles are congruent. From the markings, $\angle A$ (right angle) corresponds to $\angle X$ (right angle), $\angle B$ (angle with three marks) corresponds to $\angle Z$ (angle with three marks), and $\angle C$ (angle with two marks) corresponds to $\angle Y$ (angle with two marks). So $\angle A \cong \angle X$, $\angle B \cong \angle Z$, $\angle C \cong \angle Y$.

Step2: Analyze congruent sides

Corresponding sides are congruent. $\overline{AB}$ (three marks) corresponds to $\overline{XZ}$ (three marks), $\overline{AC}$ (two marks) corresponds to $\overline{XY}$ (two marks), $\overline{BC}$ (one mark) corresponds to $\overline{YZ}$ (one mark).

Step3: Triangle congruence statement

For $\triangle ACB$, the corresponding triangle is $\triangle XYZ$ as per the correspondence of angles and sides. So $\triangle ACB \cong \triangle XYZ$.

Answer:

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

(For the fill - in - the - blanks in the original problem:
(a) $\angle A \cong \angle \boldsymbol{X}$, $\angle B \cong \angle \boldsymbol{Z}$, $\angle C \cong \angle \boldsymbol{Y}$
(b) $\overline{AB} \cong \overline{\boldsymbol{XZ}}$, $\overline{AC} \cong \overline{\boldsymbol{XY}}$, $\overline{BC} \cong \overline{\boldsymbol{YZ}}$
(c) $\triangle ACB \cong \triangle \boldsymbol{XYZ}$)