In given figures 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. Show that: (i) ΔABM ≅ ΔPQN (ii) ΔABC ≅ ΔPQR

△ABCand△PQRin whichAB=PQ,BC=QRandAM=PN.SinceAMandPNare median of trianglesABCandPQRrespectively.Now,BC=QR∣Given⇒12BC=12QR∣Median divides opposite sides in two equal partsBM=QN... (1)Now, in△ABMand△PQNwe haveAB=PQ∣GivenBM=QN∣From (i)andAM=PN∣Given∴By SSS criterion of congruence, we have△ABM≅△PQN,which proves (i)∠B=∠Q... (2)∣Since, corresponding parts of the congruent triangle are equalNow, in△ABCand△PQRwe haveAB=PQ∣Given∠B=∠Q∣From (2)BC=QR∣Given∴by SAS criterion of congruence, we have△ABC≅△PQR, which proves (ii)