Question

δtuv and δwxy are shown below.
which statement is true?
δtuv is similar to δwxy.
δtuv is not similar to δwxy.
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 \(\angle U=180^{\circ}-(52^{\circ} + 43^{\circ})=180^{\circ}-95^{\circ} = 85^{\circ}\)

Step2: Check the angle - angle similarity criterion

In \(\triangle TUV\), angles are \(52^{\circ},43^{\circ},85^{\circ}\). In \(\triangle WXY\), \(\angle W = 52^{\circ}\) and \(\angle X=85^{\circ}\). Then \(\angle Y=180^{\circ}-(52^{\circ}+85^{\circ}) = 43^{\circ}\)
Since \(\angle T=\angle W = 52^{\circ}\), \(\angle U=\angle X = 85^{\circ}\) and \(\angle V=\angle Y=43^{\circ}\), by the AA (angle - angle) similarity criterion, \(\triangle TUV\sim\triangle WXY\)

Answer:

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