Question

In the following figures, two sides of $\Delta ABC$, $AB$ and $BC$ and median $AD$ are respectively equal to $PQ,QR$ and median $PM$ of $\Delta PQR$. Prove that: $\Delta ABC=\Delta PQR$.

Answer 1

According to question
$AB=PQ$ (given)
Median $AD$ = Median $PM$
and $BC=QR$
$\frac{1}{2}BC=\frac{1}{2}QR$
$BD=QM$
$\Delta ABD=\Delta PQM$ (by SSS congruency property)
$\angle B=\angle Q$ (by c.p.c.t)
Now in $\Delta ABC$ and $\Delta PQR$
$AB=PQ$ (given)
$\angle B=\angle Q$ (proved above)
and $BC=QR$ (given)
$\Delta ABC=\Delta PQR$ (by SAS congruency property)
Hence proved.