Question

Two sides AB, BC and median AM of one triangle ABC are respectively.
equal to sides PQ and QR and median PN of ΔPQR (See figure)
(i) ΔABM ≅ ΔPQN
(ii) ΔABC ≅ ΔPQR

Answer 1

Given,

AB = PQ
AM = PN
BC = QR
AM and PN are medium od side BC and QR respectively.
$\therefore BM=\frac{1}{2}BCQN=\frac{1}{2}QR\therefore BM=CN....(BC=QR)$
In $△$ABM and $△$PQN
AB = PQ .... (given)
AM = PN .... (given)
BM = QN
(1) $△ABN\cong △PQNbySSS.\angle ABM=\angle PQN......\left(CPCT\right)\therefore \angle ABC=\angle PQR.In△ABCand△PQR$
AB = PQ .... (given)
$\angle ABC=\angle PQR$
BC = QR .... (given)
$\therefore △ABC\cong △PQR$ by SAS Test.