Question

In ΔPQR, PQ = QR; L, M and N are the midpoints of the sides of PQ, QR and RP respectively. Prove that LN = MN.

Answer 1

Given: PQ = QR, PN = NR and PL = QL = QM = MR

To Prove: LN = MN

Proof:

In ΔPLN and ΔMRN:

PL = MR (Given)

∠LPN = ∠MRN (Angles opposite to equal sides are equal)

PN = NR (Given)

∴ ΔPLN ≅ ΔRMN (SAS congruency)

⇒ LN = MN (Corresponding parts of congruent triangles)