Question

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

Explanation:

Step1: Find ∠EFG's corresponding angle

First, calculate the third angle of $\triangle EFG$. The sum of angles in a triangle is $180^\circ$.
$\angle E = 32^\circ$, $\angle G = 90^\circ$, so $\angle F = 180^\circ - 90^\circ - 32^\circ = 58^\circ$, which matches the given $\angle F = 58^\circ$.

Step2: Analyze $\triangle HIJ$ angles

$\triangle HIJ$ is a right triangle ($\angle J = 90^\circ$). We do not know the measures of $\angle H$ or $\angle I$.

Step3: Check similarity conditions

For triangles to be similar, all corresponding angles must be equal (AA similarity). We only know both have one right angle, but no other matching angle measures are provided for $\triangle HIJ$.

Answer:

There is not enough information to determine whether the triangles are similar.