Question

in a trapezium,AB||DC and points E is the mid point of the side AD.A lines through the point E and parallel to the side AB meet the line BC in F . Prove that F is the mid point of BC.​

Answer 1

Answer:

It's a theorem - Mid point theorem. look for it in NCERT!

Answer 2

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Given ABCD is a trapezium in which AB || DC and EF||AB|| CD.

Construction Join, the diagonal AC which intersects EF at O.

To show F is the mid-point of BC.

Proof Now, in ΔADC, E is the mid-point of AD and OE || CD. Thus, by mid-point theorem, O is mid-point of AC.

Now, in ΔCBA, 0 is the mid-point of AC and OF || AB.

So, by mid-point theorem, F is the mid-point of BC.

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