Question

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


please please tell​

Answer 1

(by SAS congruence rule)

Hope this will help u.......

Answer 2

Hope it helps!!!

△ABC and△PQR in which AB=PQ,BC=QR and AM=PN.

Since AM and PN are median of triangles ABC and PQR respectively.

Now, BC=QR ∣ Given

⇒½BC = ½QR ∣ Median divides opposite sides in two equal parts

BM=QN... (1)

Now, in △ABM and△PQN we have

AB=PQ ∣ Given

BM=QN ∣ From (i)

and AM=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 equal

Now, in △ABC and△PQR we have

AB=PQ ∣ Given

∠B=∠Q ∣ From (2)

BC=QR ∣ Given

∴ by SAS criterion of congruence, we have

△ABC≅△PQR, which proves (ii)