By SAS, ∆QMP is congruent to ∆MRN.
What is congruence?
Given: MN, MP, PN are midsegments of triangle ∆QRS.
To prove: ∆QMP ≅ ∆MRN.
Let's use the Midsegment Theorem, which states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.
Proof:
MN ≅ QR (Midsegment theorem)
QM ≅ MR(M is M is midpoint of QR)
∠QMP ≅ ∠MRN (corresponding angles between parallel lines MN and QR)
∆QMP ≅ ∆MRN(Side-Angle-Side, SAS)
Therefore, by SAS, ∆QMP is congruent to ∆MRN.