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Answer 1

Step-by-step explanation:

(i) In ∆ABM and ∆PQN

AB = PQ (given)

AM = PN ( given)

BC = QR

AM and PN are medians

So, 1/2 BC = 1/2 QR

Therefore, BM = QN

Hence, ∆ABM is congruent to ∆ PQN ( by SSS )

(ii) In ∆ABC and ∆PQR

AB = PQ (given)

So, angle B = angle Q (isosceles property)

BC = QR (given)

Therefore, ∆ABC is congruent to ∆PQR ( by SAS )

I don't have the written answer, just ignore if you don't like the answer, anyway this is the correct answer.

Answer 2

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

⇒ 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)