Question

e 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: Identify Corresponding Angles

Look at the congruence marks on angles. $\angle A$ (right angle) corresponds to $\angle Y$ (right angle). $\angle B$ (double arc) corresponds to $\angle X$ (double arc). $\angle C$ (single arc) corresponds to $\angle Z$ (single arc). So $\angle A \cong \angle Y$, $\angle B \cong \angle X$, $\angle C \cong \angle Z$.

Step2: Identify Corresponding Sides

Look at the congruence marks on sides. $\overline{AB}$ (single tick) corresponds to $\overline{XY}$ (single tick). $\overline{AC}$ (double ticks) corresponds to $\overline{YZ}$ (double ticks). $\overline{BC}$ (triple ticks? Wait, no: $\overline{BC}$ has two ticks? Wait, left triangle: $\overline{AC}$ (double), $\overline{AB}$ (single), $\overline{BC}$ (two ticks? Wait, right triangle: $\overline{XY}$ (single), $\overline{YZ}$ (double), $\overline{XZ}$ (two ticks). So $\overline{AB} \cong \overline{XY}$, $\overline{AC} \cong \overline{YZ}$, $\overline{BC} \cong \overline{XZ}$.

Step3: Triangle Congruence Statement

From corresponding parts, $\triangle ACB \cong \triangle ZXY$ (matching vertices: $A\to Y$, $C\to Z$, $B\to X$? Wait, no: angle $A$ (right) is $\angle Y$, angle $B$ (double arc) is $\angle X$, angle $C$ (single arc) is $\angle Z$. So vertices: $A$ corresponds to $Y$, $C$ to $Z$, $B$ to $X$? Wait, no, let's check sides. $\overline{AC}$ (double) $\cong \overline{YZ}$ (double), $\overline{AB}$ (single) $\cong \overline{XY}$ (single), $\overline{BC}$ (two ticks) $\cong \overline{XZ}$ (two ticks). So $\triangle ACB$: $A$, $C$, $B$; $\triangle ZXY$: $Z$, $X$, $Y$? Wait, no, better to match angles: $\angle A \cong \angle Y$, $\angle B \cong \angle X$, $\angle C \cong \angle Z$. So vertex $A$ ↔ $Y$, $B$ ↔ $X$, $C$ ↔ $Z$. Thus $\triangle ACB \cong \triangle ZXY$.

Answer:

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