Question

In a $\Delta PQR$, 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

$PQ=QR=\angle PRQ=\angle RPQ$

$PQ=2PL$

$QR=2MR$

$NOWPQ=QR$

$PL=MR$

In $\Delta PLN\&\Delta RMN$

$PN=NR$

$\angle PRQ=\angle RPQ$

$PL=MR$

BY SAS RULE $\Delta PLN=\Delta RMN$

$LN=MN$( BYcpct )