3. 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 Fig. 7.40). Show that: (i) ΔABM ≅ ΔPQN (ii) ΔABC ≅ ΔPQR
Solution: Given parameters are: AB = PQ, BC = QR and AM = PN (i) ½ BC = BM and ½ QR = QN (Since AM and PN are medians) Also, BC = QR So, ½ BC = ½ QR ⇒ BM = QN In ΔABM and ΔPQN, AM = PN and AB = PQ (As given in the question) BM = QN (Already proved) ∴ ΔABM ≅ ΔPQN by SSS congruency. (ii) In ΔABC and ΔPQR, AB = PQ and BC = QR (As given in the question) ∠ABC = ∠PQR (by CPCT) So, ΔABC ≅ ΔPQR by SAS congruency
