Question

select from the drop-down menu to correctly complete the statement about the given figures. triangles pqr and mno are choose...

Explanation:

To determine the relationship between triangles \( PQR \) and \( MNO \), we analyze their angles. Both are right - angled triangles (since \( \angle P = \angle M = 90^{\circ} \)). For triangle \( PQR \), we calculate the third angle: \( 180^{\circ}-90^{\circ}-30^{\circ}=60^{\circ} \). For triangle \( MNO \), the third angle is \( 180^{\circ}-90^{\circ}-45^{\circ}=45^{\circ} \). Since the set of angles in \( PQR \) (\( 30^{\circ}, 60^{\circ}, 90^{\circ} \)) is different from the set of angles in \( MNO \) (\( 45^{\circ}, 45^{\circ}, 90^{\circ} \)), the triangles are not similar (similar triangles require corresponding angles to be equal). Also, there's no indication of equal side lengths, so they are not congruent. So the triangles are neither similar nor congruent.

Answer:

neither similar nor congruent