Question

Triangle LMN is dilated to form triangle CAB. If ∠L is congruent to angle ∠C, what other information will prove that the two triangles are similar by the AA similarity postulate?Side LN is congruent to side CB.∠N is congruent to ∠C.Side MN is congruent to side AB.∠M is congruent to ∠A.

Answer 1

To prove that the two triangles are similar by the AA similarity postulate, we need to show that two corresponding angles of the triangles are congruent.

Step-by-step explanation:

In order to prove that the two triangles are similar by the AA similarity postulate, we need to show that two corresponding angles of the triangles are congruent. We are given that angle L is congruent to angle C. To prove that the triangles are similar, we need one more piece of information. The options given are:

Side LN is congruent to side CB.

Angle N is congruent to angle C.

Side MN is congruent to side AB.

Angle M is congruent to angle A.

We can see that option 3, Side MN is congruent to side AB, is the other piece of information that will prove the triangles similar by the AA similarity postulate. Therefore, the correct answer is:

Side MN is congruent to side AB.