Question

if \\(\overline{wx} \cong \overline{wz}\\) and \\(xy = 80\\), what is \\(yz\\)?
\\(yz = \square\\)

Explanation:

Step1: Use the Hypotenuse - Leg (HL) Congruence Theorem

Since \(WY\) is perpendicular to \(XZ\) (\(\angle WYX=\angle WYZ = 90^{\circ}\)), \(WX\cong WZ\) (given), and \(WY = WY\) (common side). By the HL (Hypotenuse - Leg) congruence theorem for right - triangles (\(\triangle WYX\) and \(\triangle WYZ\)), \(\triangle WYX\cong\triangle WYZ\).

Step2: Use the property of congruent triangles

If \(\triangle WYX\cong\triangle WYZ\), then their corresponding sides are equal. That is, \(XY\cong YZ\).

Answer:

\(80\)