It is known that E and F are the midpoint of ladder ABCD, ad and BC respectively. It is proved by vector that EF is parallel to ab

Because of the trapezoid
So AB = NDC
Because AE + EF + FB = ab
Ed + EF + CF = ab
And because ed + DC + CF = EF
It is shown that 2ef = (n + 1) DC
DC//AB
So EF / / AB

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