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

Explanation:

Step1: Analyze congruent angles

In congruent triangles, corresponding angles are equal. Looking at the triangles \( \triangle ACB \) and \( \triangle YZX \) (by matching the marked sides and angles), \( \angle A \) corresponds to \( \angle X \), \( \angle B \) corresponds to \( \angle Z \), \( \angle C \) corresponds to \( \angle Y \). So \( \angle A \cong \angle X \), \( \angle B \cong \angle Z \), \( \angle C \cong \angle Y \).

Step2: Analyze congruent sides

Corresponding sides in congruent triangles are equal. \( \overline{AB} \) corresponds to \( \overline{ZX} \), \( \overline{AC} \) corresponds to \( \overline{YX} \), \( \overline{BC} \) corresponds to \( \overline{YZ} \). So \( \overline{AB} \cong \overline{ZX} \), \( \overline{AC} \cong \overline{YX} \), \( \overline{BC} \cong \overline{YZ} \).

Step3: Triangle congruence statement

From the correspondence of angles and sides, \( \triangle ACB \cong \triangle YZX \).

Answer:

(a) \( \angle A \cong \angle X \), \( \angle B \cong \angle Z \), \( \angle C \cong \angle Y \)
(b) \( \overline{AB} \cong \overline{ZX} \), \( \overline{AC} \cong \overline{YX} \), \( \overline{BC} \cong \overline{YZ} \)
(c) \( \triangle ACB \cong \triangle YZX \)