Question

Two sides AB and BC and median AD of triangle ABC are respectively equal
to sides PQ and QR and median PN of $\Delta PQR$ Then,

$\Delta ABC\equiv \Delta PQR$
If the above statement is true then mention answer as 1, else mention 0 if false

Answer 1

Given $BC=QR$
$\frac{1}{2}BC=\frac{1}{2}QR$
$BD=QN$
In $△$ ABD and PQN,
$AB=PQ$ (Given)
$BD=QN$ (Proved above)
$AD=PN$ (Given)
Thus, $△ABD\cong △PQN$ (SSS rule)
Hence, $\angle ABD=\angle PQN$ (I) (By cpct)
Now, in $△ABC$ and $△PQR$,
$AB=PQ$ (Given)
$\angle ABC=\angle PQR$ (From I)
$BC=QN$ (Given)
Thus, $△ABC\cong △PQR$ (SAS rule)