Question

△rst and △ruv are shown below. which statement is true? △rst is similar to △ruv. △rst is not similar to △ruv. there is not enough information to determine whether the

Explanation:

Step1: Calculate the third angle of \(\triangle RST\)

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle RST\), if \(\angle R = 86^{\circ}\) and \(\angle V=41^{\circ}\), then \(\angle RTS=180^{\circ}-(86^{\circ} + 41^{\circ})=53^{\circ}\)

Step2: Check for similarity using AA (Angle - Angle) criterion

In \(\triangle RST\) and \(\triangle RUV\), \(\angle R\) is common (\(\angle R=\angle R\)), and \(\angle RTS=\angle RUV = 53^{\circ}\). By the AA (Angle - Angle) similarity criterion, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Answer:

\(\triangle RST\) is similar to \(\triangle RUV\)