Question

in the diagram below, \\( \angle v \cong \angle y \\), \\( \angle w \cong \angle z \\). enter segments in the blanks provided that would result in a true equation.
answer
\\( \frac { y z } { x y } = \\)

Explanation:

Step1: Determine similar triangles

Since \(\angle V\cong\angle Y\) and \(\angle W\cong\angle Z\), by the AA (Angle - Angle) similarity criterion, \(\triangle WUV\sim\triangle XZY\).

Step2: Use the property of similar triangles

For similar triangles \(\triangle WUV\) and \(\triangle XZY\), the ratios of corresponding sides are equal. In \(\triangle XZY\), the sides are \(YZ\) and \(XY\). In \(\triangle WUV\), the corresponding sides (based on the angle - angle similarity) are \(VU\) and \(WU\). So, \(\frac{YZ}{XY}=\frac{VU}{WU}\) (corresponding sides of similar triangles are proportional).

Answer:

\(\frac{YZ}{XY}=\frac{VU}{WU}\)