Question

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

Explanation:

Step1: Calculate the third angle of $\triangle FGH$

The sum of angles in a triangle is $180^{\circ}$. For $\triangle FGH$, if two angles are $71^{\circ}$ and $47^{\circ}$, then the third angle $\angle F=180^{\circ}-(71^{\circ} + 47^{\circ})=180^{\circ}-118^{\circ}=62^{\circ}$.

Step2: Check the angle - angle similarity criterion

In $\triangle FGH$, the angles are $71^{\circ},47^{\circ},62^{\circ}$. In $\triangle IJK$, the angles are $71^{\circ},62^{\circ}$. Using the angle - angle similarity criterion (if two angles of one triangle are equal to two angles of another triangle, the triangles are similar). Since $\angle G=\angle J = 71^{\circ}$ and $\angle F=\angle I=62^{\circ}$, $\triangle FGH\sim\triangle IJK$.

Answer:

$\triangle FGH$ is similar to $\triangle IJK$.