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CBSE Class 9 Answered

If the diagonals AC, BD of a quadrilateral ABCD, intersect at O, and divide it into four triangles of equal area, Show that the quadrilateral is a parallelogram.
Asked by Topperlearning User | 17 Aug, 2017, 01:54: PM
answered-by-expert Expert Answer
ar (AOD) = ar (BOC)
 ar (AOD) + ar (AOB) = ar (BOC) + ar (AOB)
 ar (ABD) = ar (ABC)
Thus, ABD and ABC have the same base AB and have equal areas. So their corresponding altitudes must be equal.
Altitude from D of ABD = Altitude from C of ABC
DC  AB. Similarly, AD BC
Hence, quadrilateral ABCD is a parallelogram.
Answered by | 17 Aug, 2017, 03:54: PM

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