Q5 of 56 Page 78

E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.


Join BD, meeting AC at O.


Since diagonals of a parallelogram bisect each other,


OA = OC and OD = OB.


So,


OA = OC and AE = CF,



OE = OF


Now, BFDE is a quadrilateral whose diagonals bisect each other.


Hence, BFDE is a parallelogram.


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