Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of Δ PQR (see Fig. 7.40). Show that:

(i) Δ ABM Δ PQN


(ii) Δ ABC Δ PQR



It is given in the question that:

AB = PQ


BC = QR


And,


AM = PN


(i) BC = BM


And,


QR = QN (Am and PN are medians)



BC = QR


BC = QR



In


AM = PN (Given)


AB = PQ (Given)


BM = QN (Proved above)


Therefore,


By SSS axiom,



(ii) In and


AB = PQ (Given)


ABC = PQR (By c.p.c.t)


BC = QR (Given)


Therefore,


By SAS axiom,



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