CBSE Class 9 Answered
Diagonal 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 | 04 Jun, 2014, 01:23: PM
Expert Answer
Given, area (AOD) = area (BOC)
area (AOD) + area (AOB) = area (BOC) + area (AOB)
area (ABD) = area (ABC)
But, triangle ABD and ABC are on the same base AB and have equal area.
They are between the same parallels
AB||DC
Hence, ABCD is a trapezium.
[Since, a pair of opposite sides is parallel]
Answered by | 04 Jun, 2014, 03:23: PM
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