Question

triangle ghi is dilated to form new triangle jkl. if angle h is congruent to angle k, what other information will prove that the two triangles are similar by the aa similarity postulate?
angle g is congruent to angle l
side gh is congruent to side jk
angle i is congruent to angle l

Explanation:

Step1: Recall AA Similarity

AA (Angle - Angle) similarity postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Step2: Analyze Given and Required

We know that $\angle H\cong\angle K$. To apply AA similarity, we need another pair of congruent angles. Let's analyze the options:

• Option 1 (Angle G is congruent to angle L): If $\angle G\cong\angle L$ and we already have $\angle H\cong\angle K$, then we have two pairs of congruent angles ($\angle G\cong\angle L$ and $\angle H\cong\angle K$), which satisfies AA similarity.
• Option 2 (Side GH is congruent to side JK): Side congruence is related to congruent triangles (like SAS, SSS) or not directly to AA similarity which is about angles.
• Option 3 (Angle I is congruent to angle L): This does not give us a second pair of angles with the given $\angle H\cong\angle K$ to satisfy AA.

Answer:

Angle G is congruent to angle L (the first option among the given options for the congruent angle pair that satisfies AA similarity)