Question

In given figure two sides $AB,BC$ and median $AM$ of one triangle $ABC$ are respectively equal to sides $PQ$ and $QR$ and median $PN$ of $△PQR$. Show that:
$△ABM\cong △PQN$

Answer 1

Given two sides $AB,BC$ and median $AM$ of $△ABC$ are respectively

equal to sides $PQ$ and $QR$ and median $PN$ of $△PQR$.

$BC=QR$ ..Given

$\therefore \frac{1}{2}BC=\frac{1}{2}QR$

$\therefore BM=QN$ ...(1)

In $△ABM$ and $△PQN$,

$AB=PQ$ ...Given

$AM=PN$ ...Given

$BM=QN$ ...From (1)

$\therefore \Delta ABM\cong \Delta PQN$ ...SSS test $\left[henceproved\right]$