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CBSE Class 9 Answered

Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) = ar (BOC). Prove that ABCD is a trapezium.
Asked by Topperlearning User | 17 Aug, 2017, 01:58: PM
answered-by-expert Expert Answer
Draw DN  AB and CM  AB.
ar (AOD) = ar (BOC)
 ar (AOD) + ar (AOB) = ar (BOC) + ar (AOB)
 ar (ABD) = ar (ABC)
begin mathsize 12px style 1 half end styleAB DN = begin mathsize 12px style 1 half end style AB CM
DN = CM
But, DN  CM as DN and CM are perpendicular to AB. DCMN is a parallelogram.
 DC  AB
Hence, ABCD is a trapezium.
Answered by | 17 Aug, 2017, 03:58: PM

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