Question

In a ΔPQR, if PQ = QR and mid-points of three sides PQ, QR and RP are L, M and N respectively. Prove that LN = MN.

Answer 1

Given: In $∆PQR,PQ=QR$ and mid-points of three sides PQ, QR and RP are L, M and N respectively.

Now, in $∆PLN\mathrm{and}∆RMN$
$\angle P=\angle R$ (∵ PQ = QR)
PN = RN (N is mid-point of PR)
PL = RM (PQ = QR and L and M are mid-points of PQ and RQ respectively )
$\therefore ∆PLN\cong ∆RMN$ (By SAS)
Thus, by corresponding parts of congruent triangles, we have
LN = MN