Question

show that the two triangles are similar and choose a similarity statement.
∠q≅∠
∠n≅∠
, so △lnq∼△mnp.

Explanation:

Step1: Recall the AA (Angle - Angle) similarity criterion

If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
We are given that \(\angle Q\cong\angle N\). Also, \(\angle QLN\) and \(\angle NMP\) are corresponding angles (by the parallel - line property, since the two lines with the red arrow - heads are parallel).

Step2: Match the angles for the similarity statement

For \(\triangle LNQ\) and \(\triangle MNP\), we have \(\angle Q\cong\angle N\) and \(\angle QLN\cong\angle NMP\) (by AA similarity criterion). When writing the similarity statement, the order of the vertices must correspond to the congruent angles.

Answer:

\(\triangle LNQ\sim\triangle MNP\) (using the AA similarity criterion as \(\angle Q\cong\angle N\) and \(\angle QLN\cong\angle NMP\))