Question

∠uzv ≅ ∠xwy, ∠vuz ≅ ∠wxy, and \overline{yz} ≅ \overline{vw}. complete the proof that \overline{uv} ≅ \overline{xy}.

Explanation:

Step1: Prove triangles congruent

Given \(\angle UZV\cong\angle XWY\), \(\angle VUZ\cong\angle WXY\), and \(VZ = WY\) (from step 7). By the Angle - Angle - Side (AAS) congruence criterion, \(\triangle UZV\cong\triangle XWY\).

Step2: Use congruent triangles property

If two triangles \(\triangle UZV\) and \(\triangle XWY\) are congruent, then their corresponding sides are equal. So, \(UV\) and \(XY\) are corresponding sides.

Answer:

\(\triangle UZV\cong\triangle XWY\) (AAS); Corresponding parts of congruent triangles are congruent. So, \(\overline{UV}\cong\overline{XY}\)