Question

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

Explanation:

Step1: Calculate ∠DGF in △DFG

Sum of angles in a triangle is $180^\circ$.
$\angle DGF = 180^\circ - \angle F - \angle D = 180^\circ - 44^\circ - 103^\circ = 33^\circ$

Step2: Calculate ∠DHE in △DHE

Sum of angles in a triangle is $180^\circ$.
$\angle DHE = 180^\circ - \angle DEH - \angle D = 180^\circ - 33^\circ - 103^\circ = 44^\circ$

Step3: Compare corresponding angles

In △DFG and △DHE:
$\angle D = \angle D$ (common angle), $\angle F = \angle DHE = 44^\circ$, $\angle DGF = \angle DEH = 33^\circ$. All corresponding angles are congruent, so the triangles are similar by AA similarity criterion.

Answer:

$\triangle DFG$ is similar to $\triangle DHE$.