Question

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Answer 1

Answer:

ab = pq

BM=qn

am=pn

therefore by sss criteria triangle ABM is similar to pqn

ab = pq

BC= qr

ac=PR

therefore by sss criteria triangle ABC is congruent to triangle pqr

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Answer 2

Answer:

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• ∆ABM is congruent to ∆PQN by the Side Side Side (SSS) criteria of congruency

• ∆ABC is congruent to ∆PQR by the Side Angle Side (SAS) criteria of congruency

Step-by-step explanation:

Given:-

• AB = PQ
• BC = QR
• Medians AM and PN are equal

To prove:-

• ∆ABM is congruent to ∆PQN

• ∆ABC is congruent to ∆PQR

Proof:-

In ∆ABM and ∆PQN

• AB = PQ (Given)

• BM = QN [ As given that BC = QR and that AM and PN are medians ( therefore, M and N are the mid points of BC and PR)]

• AM = PN ( Given)

Therefore, By SSS criteria of congruency the triangles are congruent.

=> / B = / Q ( By CPCT) .......(i)

In ∆ABC and ∆PQR

• AB = PQ ( given)

• / B = / Q [ from (i) ]

• BC = QR (given)

Therefore, By SAS criteria of congruency, the triangles are congruent.

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