Question

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

Answer 1

PQ=QR

L,MN are midpoints of PQ,QR,PR respctively

⇒PL=PQ=QM=MR.............................(i)

and ∠QPR=∠QRP(angles opp. to equal sides)......................................(ii)

in ΔLPN and Δ MNR

PL=MR(from (i))

∠LPN=∠MRN(from (ii))

PN=NR( N is midpoint)

∴ΔLPN≅ΔMNR(By SAS congruency)

⇒LN=MN(corresponding sides)

Hence Proved