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

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

Answers (1)

Given : ABCD is a parallelogram and AE = CF
To prove: OE = OF

Proof: Join BD and CA
Here OA = OC and OD = OB   [ABCD is parallelogram]
\Rightarrow OA = OC …..(1)
And AE = CF …..(2)     {given}
OA -AE = OC - CF {by subtracting 2 from 1}
OE = OF
Hence, BFDE is a parallelogram.

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