Given that ∠MPN is a right angle, we know that MP and NP are perpendicular to each other. Since NP is also a perpendicular bisector of MO, it bisects MO at a 90-degree angle.
Also given that NP is a perpendicular bisector of MO, we know that NP is equidistant from M and O. Therefore, NP is the midpoint of MO and so MN = NO.
Since MP and NP are perpendicular and MN = NO, it follows that △MNP is similar to △ONP.
Therefore, we can conclude that △MNP ≅ △ONP