Question

determine whether the pair of triangles is similar. explain your reasoning.

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. In the figure, $\angle GIH$ and $\angle KIL$ are vertical angles. So, $\angle GIH=\angle KIL$.

Step2: Check for another pair of equal angles

We are given that $\angle H=\angle L$.

Step3: Apply AA (Angle - Angle) similarity criterion

If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. For $\triangle GIH$ and $\triangle KIL$, since $\angle H=\angle L$ and $\angle GIH=\angle KIL$, by AA similarity criterion, $\triangle GIH\sim\triangle KIL$.

Answer:

$\triangle GIH\sim\triangle KIL$ by AA Similarity.