The Total solution for NCERT class 6-12
DiagonalsAC and BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) =ar (BOC). Prove that ABCD is a trapezium.
It is given that
Area (ΔAOD) = Area (ΔBOC)
Area (ΔAOD) + Area (ΔAOB)= Area (ΔBOC) + Area (ΔAOB)
Area (ΔADB) = Area (ΔACB)
We know that triangles onthe same base having areas equal to each other lie between the same parallels.
Therefore, thesetriangles, ΔADB and ΔACB, are lying between the same parallels.
i.e., AB || CD
Therefore,ABCD is a trapezium.