Question

the two polygons below are similar.
complete the similarity statement

Explanation:

Step1: Identify corresponding angles

In similar polygons, corresponding angles are equal. In the first polygon \(VWXY\), \(\angle V\) and \(\angle X\) are equal (let's assume they are the ones corresponding to \(\angle E\) and \(\angle G\) in the second polygon \(GFEH\)). \(\angle W = 68^{\circ}\) corresponds to \(\angle G\) (since \(68^{\circ}\) and the other angles in the second polygon \(112^{\circ}\) - and \(68 + 112=180\) for adjacent angles in a parallelogram - but in terms of similarity, we match by measure. \(\angle F=\angle Y = 112^{\circ}\), \(\angle H=\angle Y = 112^{\circ}\), \(\angle E=\angle V\), \(\angle G=\angle W\).

Step2: Match the order of vertices

Starting with the angle \(\angle W = 68^{\circ}\) (which corresponds to \(\angle G = 68^{\circ}\)), then moving to the next angle. The order of vertices for the first polygon is \(V - W - X - Y\). For the second polygon, since \(\angle G\) corresponds to \(\angle W\), then \(\angle F\) (which is \(112^{\circ}\)) corresponds to \(\angle Y\) ( \(112^{\circ}\) in \(VWXY\)), \(\angle E\) corresponds to \(\angle V\), \(\angle H\) corresponds to \(\angle X\). So the similarity statement is \(VWXY\sim GFEH\)

Answer:

\(VWXY\sim GFEH\)