Question

Gerry Drew triangle JKL and triangle MNP so that angle K is congruent to angle N, angle A is congruent to angle P, side JK equals 6, and side MN equals 18. Are triangles JKL and MNP similar?

A) Yes
B) No

Answer 1

Triangles JKL and MNP are similar because angle K is congruent to angle N and angle A is congruent to angle P, and the corresponding sides are in proportion.

Step-by-step explanation:

Triangles JKL and MNP are similar.

Given that angle K is congruent to angle N and angle A is congruent to angle P, we can use the Angle-Angle (AA) Similarity Postulate to prove that the triangles are similar.

Since angle K is congruent to angle N and angle A is congruent to angle P, we know that angle KJL is congruent to angle MNL and angle JKL is congruent to angle MNP.

Additionally, we are given that side JK equals 6 and side MN equals 18. By comparing the corresponding sides, we can set up the proportion:

JK / MN = JL / MP

Substituting the given values, we have:

6 / 18 = JL / MP

Simplifying the proportion, we get:

1 / 3 = JL / MP

This shows that the corresponding sides are in proportion, which further supports the similarity of the triangles.