Question -
Answer -
Given : In тИЖPQR, PQ = QR
L, M and N are the mid-points of sides PQ, QR and RP respectively. Join LM, MN and LN
To prove : тИаPNM = тИаPLM
Proof : In тИЖPQR,
тИ╡ M and N are the mid points of sides PR and QR respectively
тИ┤ MN || PQ and MN = 
PQ тАж(i) тИ┤ MN = PL
Similarly, we can prove that
LM = PN
Now in тИЖNML and тИЖLPN
MN = PL (Proved)
LM = PN (Proved)
LN = LN (Common)
тИ┤ тИЖNML = тИЖLPN (SSS axiom)
тИ┤ тИаMNL = тИаPLN (c.p.c.t.)
and тИаMLN = тИаLNP (c.p.c.t.)
тЗТ тИаMNL = тИаLNP = тИаPLM = тИаMLN
тЗТ тИаPNM = тИаPLM