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 b a c \cong \triangle \square \\)

Explanation:

Step1: Identify corresponding angles

Since the triangles are congruent and corresponding parts are marked. For angles, \(\angle A\) corresponds to \(\angle Z\) (as per the markings on the non - equal sides adjacent to the angles). \(\angle B\) corresponds to \(\angle X\) (as per the markings on the sides opposite to the angles in the congruent triangles). \(\angle C\) corresponds to \(\angle Y\) (as per the markings on the vertex angles).

Step2: Identify corresponding sides

For sides, \(\overline{AB}\) corresponds to \(\overline{ZX}\) (as per the markings of the number of segments on the sides). \(\overline{AC}\) corresponds to \(\overline{ZY}\) (as per the single - segment markings on the sides). \(\overline{BC}\) corresponds to \(\overline{XY}\) (as per the double - segment markings on the sides).

Step3: Write the triangle congruence statement

For \(\triangle BAC\), when we match the vertices: \(B\) with \(X\), \(A\) with \(Z\), \(C\) with \(Y\). So \(\triangle BAC\cong\triangle XZY\)

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) \(\triangle BAC\cong\triangle XZY\)