Question

is $\triangle mno$ similar to $\triangle pqo$?

Explanation:

Step1: Identify right angles

Both $\triangle MNO$ and $\triangle PQO$ have a right angle ( $\angle MNO$ and $\angle PQO$ are right angles, as $MN \perp ON$ and $PQ \perp OQ$). So, one pair of angles is equal (both $90^\circ$).

Step2: Check the included angle (vertical angles)

$\angle MON$ and $\angle POQ$ are vertical angles, so they are equal. By the AA (Angle - Angle) similarity criterion, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar. Since we have two pairs of equal angles (right angle and vertical angle), the triangles are similar.

Answer:

Yes