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) ∠b ≅ ∠
(c) ∠c ≅ ∠
(d) \\(\overline{ab} \cong \overline{}\\)
(e) \\(\overline{ac} \cong \overline{}\\)
(f) \\(\overline{bc} \cong \overline{}\\)
(g) \\(\triangle abc \cong \triangle \\)

Explanation:

Step1: Identify Corresponding Angles

In congruent triangles, corresponding angles are equal. Looking at the markings: $\angle A$ (single arc) corresponds to $\angle Y$ (single arc), $\angle B$ (double arc) corresponds to $\angle X$ (double arc), $\angle C$ (triple arc) corresponds to $\angle Z$ (triple arc). So $\angle A \cong \angle Y$, $\angle B \cong \angle X$, $\angle C \cong \angle Z$.

Step2: Identify Corresponding Sides

Corresponding sides are marked with equal tick marks. $AB$ (two ticks) corresponds to $YX$ (two ticks), $AC$ (one tick) corresponds to $YZ$ (one tick), $BC$ (three ticks) corresponds to $XZ$ (three ticks). So $\overline{AB} \cong \overline{YX}$, $\overline{AC} \cong \overline{YZ}$, $\overline{BC} \cong \overline{XZ}$.

Step3: Write Congruence Statement

Using corresponding vertices, $\triangle ABC \cong \triangle YXZ$ (matching angles and sides).

Answer:

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