Question

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

Explanation:

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

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle TUV\), if \(\angle T = 52^{\circ}\) and \(\angle V=43^{\circ}\), then \(\angle U=180^{\circ}-(52^{\circ} + 43^{\circ})=85^{\circ}\)

Step2: Compare angles of \(\triangle TUV\) and \(\triangle WXY\)

In \(\triangle TUV\), angles are \(52^{\circ},43^{\circ},85^{\circ}\). In \(\triangle WXY\), \(\angle W = 52^{\circ}\), \(\angle X=85^{\circ}\). Then \(\angle Y=180^{\circ}-(52^{\circ}+85^{\circ}) = 43^{\circ}\). Since the three angles of \(\triangle TUV\) are equal to the three angles of \(\triangle WXY\) (by AA - Angle - Angle similarity criterion, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar)

Answer:

\(\triangle TUV\) is similar to \(\triangle WXY\)