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

Given:

In a $\triangle PQR$, $PQ = QR$ and $L, M$ and $N$ are the mid-points of the sides $PQ, QR$ and $RP$ respectively. 

To do:

We have to prove that $LN = MN$.

Solution:

In $\triangle LPN$ and $\triangle MRH$,

$PN = RN$               (Since $M$ is the mid point of $PR$)

$LP = MR$                 

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

Therefore, by SAS axiom

$\triangle LPN \cong \triangle MRH$

This implies,

$LN = MN$              (CPCT)

Hence proved.

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Updated on: 10-Oct-2022

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