Question

2.
Р
Two sides AB, BC and median
AM of one triangle ABC are
respectively equal to sides PQ and
QR and median PN of triangle PQR (See
figure). Show that:
(i) triangle ABM is congruent to the triangle PQN
(ii) triangleABC is congruent to the triangle PQR​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

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

1/2 BC=1/2QR ∣ 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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