Question

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

Answer:

GIVEN : PQ = QR , L is mid point of PQ,M is midpoint of QR and N is the mid point of PR  

Consider ΔPRQ and ΔRPQ

= PQ = QR ⇒∠PRQ =∠RPQ

= QR = 2MR

= PQ = QR ⇒ PL =MR

∴  In ΔPNL and ΔRNM  ( In a Triangle opposite angles are Equal)

= NP = RN

∴ By SAS Congruence Rule,

= ΔPRQ ≅ ΔRPQ  

In which,

⇒ PL = MR [CPCT]