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A B C D is a parallelogram. A D is a pro...

`A B C D` is a parallelogram. `A D` is a produced to `E` so that `D E=D C` and `E C` produced meets `A B` produced in `Fdot` Prove that `B F=B Cdot`

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`ABCD` is A parallelogram
`BF=BC`
In `/_\DCE,DE=DC`(given)
`/_DCE=/_DEC`(1)(Equal sides have equal is opposite to them)
`AB∥CD,/_DCE=/_BFC`(2) (pair of corresponding `/_S`)
Form (1) and (2),`/_DEC=/_BFC`
In `/_\AEF,/_AEF=/_AFE`
`AF=AE`
`=>AB+BF=AD+DE`
`BF=AD (AB=CD=DE)`
`=>BF=BC (AD=BC)` Hence proved.
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