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: 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 all three pairs of corresponding angles are equal ($\angle T=\angle W = 52^{\circ}$, $\angle U=\angle X = 85^{\circ}$, $\angle V=\angle Y=43^{\circ}$), by the AA (angle - angle) similarity criterion, the two triangles are similar.

Answer:

$\triangle TUV$ is similar to $\triangle WXY$.