Question

Two sides AB, BC and median
AM of one triangle ABC are
respectively equal to sides PQ and
QR and median PN of ∆PQR (See
figure). Show that:
∆ABC = ∆PQR
​

Answer 1

Answer:

AM is perpendicular to BC and PN is perpendicular to QR

Answer 2

Answer:

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

Now, BC=QR ∣ Given

⇒

2

1

BC=

2

1

QR ∣ 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)