MP is congruent to NO by CPCTC, CPCTC states that if two triangles are congruent, then every corresponding part of one triangle is congruent to the other.
MN is congruent to OP: Given.
Triangle MPN is congruent to triangle ONP by the theorem of SAS: if two sides and the included angles of one triangle are equal to two sides and the included angle of the other one, they are congruent.
PN is congruent to PN by the reflexive property of congruence, it states that an angle, line, segment or shape is always congruent to itself.