Question

Two sides AB and BC and median AM of one triangle ABC are respectively equal to side PQ and QR and median PN of ∆PQR (see figure). Show that

(i) ∆ABM = ∆PQN

(ii) ∆ABC = ∆PQR

Answer 1

(i) In ∆’s ABM and PQN

AB = PQ (given)

AM = PN (given)

and BC = QR (given)

=> 1/2BC = 1/2QR

=> BM = QN

∴ ∆ABM ≅ ∆PQN

(by SSS congruency rule)

(ii) In ∆ABC and ∆PQR

∵ ∆ABM ≅ ∆PQN [proved in (i)]

=> ∠B = ∠Q (by c.p.c.t)

AB = PQ (given)

BC = QR (given)

∴ ∆ABC ≅ ∆PQR

(by SAS congruency rule)