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

Congruent triangles have matching angles. By looking at the marked angles (the arcs), \(\angle A\) corresponds to \(\angle Z\), \(\angle B\) corresponds to \(\angle X\), and \(\angle C\) corresponds to \(\angle Y\).

Step2: Identify corresponding sides

Congruent triangles have matching sides. The tick - marks show that \(\overline{AB}\) corresponds to \(\overline{ZX}\), \(\overline{AC}\) corresponds to \(\overline{ZY}\), and \(\overline{BC}\) corresponds to \(\overline{XY}\).

Step3: Complete the congruence statement

For \(\triangle CBA\), we match the vertices. \(C\) corresponds to \(Y\), \(B\) corresponds to \(X\), and \(A\) corresponds to \(Z\). So \(\triangle CBA\cong\triangle YXZ\)

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) \(\triangle CBA\cong\triangle YXZ\)