Question

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

Explanation:

Step1: Identify right angles

In $\triangle DEF$ and $\triangle FGH$, $\angle D$ and $\angle F$ (wait, $\angle D$ is a right angle? Wait, looking at the diagram, $ED \perp DF$ (since $ED$ has one mark and $DF$ is horizontal, so $\angle D = 90^\circ$), and $GF \perp FH$ (since $GF$ has one mark and $FH$ is horizontal, so $\angle F = 90^\circ$). So both triangles are right - angled.

Step2: Check for proportional sides and equal angles

We can see that the sides with one mark: $ED$ and $GF$ are corresponding, and the sides with two marks: $EF$ and $GH$ are corresponding. Also, $\angle D=\angle F = 90^\circ$, and 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. Here, we have a right angle in each triangle, and we can also check the sides. The ratio of the sides with one mark and the sides with two marks should be equal, and the included angles (the right angles) are equal. So by AA similarity, $\triangle DEF\sim\triangle FGH$.

Answer:

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