Question

△lmn and △nop are shown below.
which statement is true?
△lmn is similar to △nop.
△lmn is not similar to △nop.
there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Identify corresponding angles

We know $\angle L$ and $\angle ONP$ are congruent (marked by the same angle indicator, so $\angle L = \angle ONP$). $\angle LNM$ and $\angle ONP$ are vertical angles, so $\angle LNM = \angle ONP$, which means $\angle L = \angle LNM$? No, correction: $\angle L$ corresponds to $\angle ONP$ (corresponding angles from the parallel-like angle mark), and $\angle LNM$ is vertical to $\angle ONP$? No, actually, $\angle L$ and $\angle ONP$ are equal (given by the matching arrows, so they are corresponding equal angles). We only know one pair of equal angles ($\angle L = \angle ONP$) and one angle $\angle P = 67^\circ$, but we have no information about the other angles of $\triangle LMN$ or the side ratios.

Step2: Check similarity criteria

Similarity requires 2 pairs of congruent angles (AA), or proportional sides with included congruent angle (SAS), or all proportional sides (SSS). We only have confirmation of one pair of equal angles, and no side length information or a second confirmed equal angle pair.

Answer:

There is not enough information to determine whether the triangles are similar.