Question 37585: PQRS in a parallelogram,Q and S are joined to any point M on the diagonal PR of the parallelogram.Prove that area of the triangle PQM=area of triangle PSM
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! PQRS in a parallelogram,Q and S are joined to any point M on the diagonal PR of the parallelogram.Prove that area of the triangle PQM=area of triangle PSM
IN THE DIAGRAM ,DRAW ST FROM S AND QV FROM Q ,PERPENDICULAR TO PR THE DIAGONAL ,MEETING IT AT T AND V RESPECTIVELY.
NOW PARALLELOGRAM PQRS IS DIVIDED IN TO 2 EQUAL PARTS BY DIAGONAL PR(EASILY PROVED BY SSS ..PQ=RS,PR=PR AND PS=QR)
SO AREA OF TRIANGLE PRS=AREA OF TRIANGLE PQR..
THEY HAVE SAME BASE PR.
HENCE THEIR ALTITUDES TO THAT SAME BASE ARE EQUAL
THAT IS ST=QV
NOW TRIANGLES PQM AND PSM HAVE SAME BASE PM.
THEIR ATITUDES TO THAT BASE ST AND QV ARE EQUAL.HENCE AREA OF TRIANGLE PQM=AREA OF TRIANGLE PSM
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