Given: QN = RN and MN=NP
Given: m∠1=m∠2
Since SN is perpendicular to MP.
[tex]\implies m\angle3=m\angle4\text{ (Complementary angles of }\angle1\text{ and }\angle2)[/tex]
Given: MN=NP
• Therefore triangles QNM is similar to triangle RNP by the SAS Congruence Theorem.
• Since two corresponding sides are equal, the triangles are in fact equal triangles.
Thus, the length of the third corresponding sides QM and RP must also be equal by CPCTC.
