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) $\triangle cba \cong \triangle \square$

Explanation:

Step1: Match congruent angles

Look at marked corresponding angles:

• $\angle A$ matches $\angle Z$
• $\angle B$ matches $\angle Y$
• $\angle C$ matches $\angle X$

Step2: Match congruent sides

Look at marked corresponding sides:

• $\overline{AB}$ matches $\overline{ZY}$
• $\overline{AC}$ matches $\overline{ZX}$
• $\overline{BC}$ matches $\overline{YX}$

Step3: Write congruence statement

Map vertices from $\triangle CBA$ to corresponding vertices: $C \to X$, $B \to Y$, $A \to Z$

Answer:

(a)
$\angle A \cong \angle Z$
$\angle B \cong \angle Y$
$\angle C \cong \angle X$

(b)
$\overline{AB} \cong \overline{ZY}$
$\overline{AC} \cong \overline{ZX}$
$\overline{BC} \cong \overline{YX}$

(c)
$\triangle CBA \cong \triangle XYZ$