Question

Sides AB and BC and median AD of a ∆ABC are respectively proportional to sides PQ and QR and median PM of a ∆PQR. Show that ∆ ABC ≅ ∆ PQR

Class 10 ​

Answer 1

Answer:

△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

⇒

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)

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Answer 2

QUESTION:-

Sides AB and BC and median AD of a ∆ABC are respectively proportional to sides PQ and QR and median PM of a ∆PQR. Show that ∆ ABC ≅ ∆ PQR.....

ANSWER:-

I TRIED SO , FAR