Question

In a $\Delta PQR,ifPQ=QR$ and L, M and N are the mid-points of the sides PQ, QR and RP respectively. Prove that LN = MN.

Answer 1

Given : in $\Delta PQR,PQ=QR$

L, M and N are the mid points of the sides PQ, QR and PR respectively

To prove : LM = MN

Proof : in $\Delta LPNand\Delta MRN$

PN = RN ($\because$ M is mid point of PR)

LP = MR (Half of equal sides)

$\angle P=\angle R$ (Angles opposite to equal sides)

$\therefore \Delta LPN\cong \Delta MRN$ (SAS axiom)

$\therefore LN=MN$ (c.p.c.t.)