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) ∠a ≅ ∠
∠b ≅ ∠
∠c ≅ ∠
(b) overline{ab} ≅ overline{}
overline{ac} ≅ overline{}
overline{bc} ≅ overline{}
(c) δcba ≅ δ

Explanation:

Step1: Analyze congruent angles

In congruent triangles, corresponding angles are equal. For $\triangle CBA$ and $\triangle YXZ$ (by matching marked angles and sides), $\angle A$ corresponds to $\angle Z$, $\angle B$ corresponds to $\angle X$, $\angle C$ corresponds to $\angle Y$. So $\angle A\cong\angle Z$, $\angle B\cong\angle X$, $\angle C\cong\angle Y$.

Step2: Analyze congruent sides

Corresponding sides are equal. $\overline{AB}$ corresponds to $\overline{XZ}$, $\overline{AC}$ corresponds to $\overline{YZ}$, $\overline{BC}$ corresponds to $\overline{XY}$. So $\overline{AB}\cong\overline{XZ}$, $\overline{AC}\cong\overline{YZ}$, $\overline{BC}\cong\overline{XY}$.

Step3: Write congruence statement

The congruence statement for $\triangle CBA$ is $\triangle CBA\cong\triangle YXZ$ (matching corresponding vertices).

Answer:

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