Question

triangles identifying and naming congruent parts of congruent triangles 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 b a c \cong \triangle \square \\)

Explanation:

Step1: Identify corresponding angles

In congruent triangles, angles with the same markings are congruent.

• $\angle A$ has the same marking as $\angle Z$, so $\angle A\cong\angle Z$.
• $\angle B$ has the same marking as $\angle X$, so $\angle B\cong\angle X$.
• $\angle C$ has the same marking as $\angle Y$, so $\angle C\cong\angle Y$.

Step2: Identify corresponding sides

Sides with the same markings are congruent.

• $\overline{AB}$ has the same marking as $\overline{ZX}$, so $\overline{AB}\cong\overline{ZX}$.
• $\overline{AC}$ has the same marking as $\overline{ZY}$, so $\overline{AC}\cong\overline{ZY}$.
• $\overline{BC}$ has the same marking as $\overline{XY}$, so $\overline{BC}\cong\overline{XY}$.

Step3: Complete the triangle congruence statement

For $\triangle BAC$ and $\triangle ZXY$, using the order of corresponding vertices (from angle - side - angle correspondence based on congruent parts):
$\triangle BAC\cong\triangle ZXY$

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) $\triangle BAC\cong\triangle ZXY$