If two sides AB and BC, and the median AD of ABC are correspondingly equal to the two sides PQ and QR, and the median PM of PQR. Prove that ABCPQR.


Answer:


Step by Step Explanation:
  1. We are given that AB=PQ, BC=QR, and AD=PM.

    Let us now draw the triangles and mark the equal sides and medians.
      A B C D P Q R M
  2. We need to prove that ABCPQR.
  3. It is given that BC=QR12BC=12QRBD=QM(1) [As the median from a vertex of a triangle bisects the opposite side.]  Now, in ABD and PQM, we have AD=PM[Given]AB=PQ[Given]BD=QM[From (1)] ABDPQM[By SSS criterion]
  4. As corresponding parts of congruent triangles are equal, we have B=Q   (2)
  5. In ABC and PQR, we have BC=QR[Given]AB=PQ[Given]B=Q[From (2)] ABCPQR[By SAS criterion]
    Hence Proved.

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