Question

Sides $AB$ and $AC$ and median $AD$ of a $\Delta$ABC are respecting proportional to sides $PQ$ and $PR$ and median $PM$ of another $\Delta$ PQR. Show that $△ABC\sim △PQR$.

Answer 1

$AD=\frac{2\left(AB\right)\left(AC\right)}{AB+AC}\cos \frac{A}{2},PM=\frac{2\left(PQ\right)\left(PR\right)}{PQ+PR}\cos \frac{P}{2}$

In $△ABC,△PQR$

$\because AB=kPQ,AC=kPR,AD=kPM⟹A=P$

By $S.A.S$ criteria

$△ABC\sim △PQR$