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 would prove the triangles are similar based on the

Explanation:

Step1: Recall triangle similarity criteria

Triangle similarity can be proven by AA (Angle - Angle), SAS (Side - Angle - Side), or SSS (Side - Side - Side) criteria. We know that \(\angle H=\angle M\). If we can show another pair of corresponding angles are equal, we can use AA. For example, if \(\angle G = \angle L\) (or \(\angle F=\angle K\)), then with \(\angle H=\angle M\), by AA similarity criterion, the triangles \(\triangle FGH\) and \(\triangle KLM\) will be similar.

Step2: Determine the similarity criterion

If we show that another pair of corresponding angles are equal (e.g., \(\angle G=\angle L\) or \(\angle F = \angle K\)), then since we already have \(\angle H=\angle M\), by the AA (Angle - Angle) similarity postulate, which states that if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.

Answer:

First drop - down: \(\boldsymbol{\angle G=\angle L}\) (or \(\boldsymbol{\angle F=\angle K}\))
Second drop - down: \(\boldsymbol{AA}\) (Angle - Angle) Similarity Criterion