Q10 of 33 Page 108

In two parallelograms ABCD and AECF, AC is a diagonal. If B, E, D, F are not collinear, then let us prove that, BEDF is a parallelogram.

Two parallelograms ABCD and AECF are shown in different colors and the third quadrilateral BEDF is shown in different color


Their intersection of diagonals is marked as point O



EF = OF … diagonal of parallelogram AECF bisect each other … (i)


DO = OB … diagonal of parallelogram ABCD bisect each other … (ii)


Now consider quadrilateral DEFB


Diagonals are EF and BD and from (i) and (ii) we can say that they bisect each other


As diagonals bisect each other the quadrilateral is a parallelogram


Hence, DEFB is a parallelogram


Hence proved


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