Question

Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see the given figure).
Is $\Delta ABM\cong \Delta PQN$?

• A. Yes
• B. No

Answer 1

The correct option is A Yes

In $\Delta$ABC, AM is the median to BC
$\therefore BM=\frac{1}{2}BC$
In $\Delta$PQR, PN is the median to QR
$\therefore QN=\frac{1}{2}QR$
However BC = QR
$\Rightarrow$ BM = QN
In $\Delta$ABM and $\Delta$PQN, we have
AB=PQ (Given)
AM=PN (Given)
BM = QN (Proved above)
$\therefore \Delta ABM\cong \Delta PQN$ (By SSS congruence rule)
$\Rightarrow \angle ABM=\angle PQN$ (By CPCT)