Question

triangle fgh and triangle klm are shown below. the measure of ∠h is equal to the measure of ∠m. use the drop - down menus to provide additional information that would prove that the two triangles are similar. showing that angle f = angle k would prove the triangles are similar based on the drop - down menu with options: angle - side criterion, sum of interior angles criterion, angle - angle criterion

Explanation:

Step1: Recall Similarity Criteria

To prove two triangles are similar, we can use criteria like AA (Angle - Angle), SAS (Side - Angle - Side), SSS (Side - Side - Side). The AA criterion states that if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.

Step2: Analyze Given Angles

We know that $\angle H=\angle M$. If we show that $\angle F = \angle K$, then we have two pairs of congruent angles ($\angle H=\angle M$ and $\angle F=\angle K$). By the AA (Angle - Angle) similarity criterion, the triangles $\triangle FGH$ and $\triangle KLM$ will be similar.

Answer:

Showing that $\boldsymbol{\angle F=\angle K}$ would prove the triangles are similar based on the $\boldsymbol{\text{angle - angle (AA) criterion}}$.