The Total solution for NCERT class 6-12
Two sides AB and BC and median AM of one triangle ABC arerespectively equal to sides PQ and QR and median PN of ΔPQR (see the given figure).Show that:
(i) ΔABM ≅ ΔPQN
(i) In ΔABC, AM is the median to BC.
In ΔPQR, PN is the median to QR.
However, BC = QR
⇒ BM = QN … (1)
In ΔABM and ΔPQN,
AB = PQ (Given)
BM = QN [From equation (1)]
AM = PN (Given)
∴ ΔABM ≅ ΔPQN (SSS congruence rule)
∠ABM = ∠PQN (By CPCT)
∠ABC = ∠PQR … (2)
(ii) In ΔABC and ΔPQR,
∠ABC = ∠PQR [From equation (2)]
BC = QR (Given)
⇒ ΔABC ≅ ΔPQR (By SAS congruence rule)