Question

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

Explanation:

Step1: Calculate angles in \(\triangle UVW\)

In \(\triangle UVW\), we know one angle is \(75^{\circ}\) and another is \(45^{\circ}\). Using the angle - sum property of a triangle (\(\angle V+\angle U+\angle W = 180^{\circ}\)), we find \(\angle V=180^{\circ}-(75^{\circ}+45^{\circ}) = 60^{\circ}\).

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

In \(\triangle YXW\), \(\angle X = 60^{\circ}\). In \(\triangle UVW\), \(\angle V = 60^{\circ}\). Also, \(\angle VWU\) and \(\angle XWY\) are vertical angles (so they are equal). 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:

\(\triangle UVW\) is similar to \(\triangle YXW\)