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In Figure, A B C D isa trapezium in whic...

In Figure, `A B C D` isa trapezium in which side `A B` is a parallel to side `D C` and `E` is the mid-point of side `A D`. If `F` is a point on the side `B C` such that the segment `E F` is parallel to side `D C` . Prove that `F` is the mid point of `B C` and `E F=1/2(A B+D C)`.

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