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{a b} \cong \overline{\square} \\) \\( \angle b \cong \angle \square \\) \\( \overline{a c} \cong \overline{\square} \\) \\( \angle c \cong \angle \square \\) \\( \overline{b c} \cong \overline{\square} \\) (c) \\( \triangle c b a \cong \triangle \square \\)

Explanation:

Step1: Identify corresponding angles

For congruent triangles, angles with same markings are congruent.

• $\angle A\cong\angle Z$ (marked with one arc)
• $\angle B\cong\angle Y$ (marked with one arc)
• $\angle C\cong\angle X$ (marked with one arc)

Step2: Identify corresponding sides

Sides with same markings are congruent.

• $\overline{AB}\cong\overline{ZY}$ (marked with one tick)
• $\overline{AC}\cong\overline{XZ}$ (marked with one tick)
• $\overline{BC}\cong\overline{XY}$ (marked with one tick)

Step3: Complete triangle congruence statement

Using the order of vertices for congruent angles and sides.
$\triangle CBA\cong\triangle XZY$

Answer:

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