Q. In the following figures, the sides AB and BC and the median AD of triangle ABC are respectively equal to the sides PQ and QR  and median PS of triangle PQR. Prove that triangle ABC is congruent to triangle PQR

Dear Student,
As we know,AD is the median to BC of ABCtherefore, BD=2BCand, PS is the median to QR of PQRtherefore, QS=2QRHowever,BC=QR2BC=2QR  BD=QS ---1Now,In ABD and PQSAB=PQ givenBD=QS from 1AD=PS giventherefore by SSS congruency rule AMDPQS and ABD=PQS  By CPCTso, ABC=PQR ----2Now,In ABC and PQR,AB=PQ givenABC=PQR from 2BC=QR giventherefore,by SAS congruency rule ,ABCPQR


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