# ABCD is a trapezium with ab||dc. e and f are points on non-parallel sides ad and bc respectively such that EF||AB . prove that AE/ED=BE/FC

Given: ABCD is a trapezium where AB||DC. E and F are points on non-parallel sides AD and BC respectively.

To Prove: AE/ED = BF/FC

Proof: Given AB||DC and EF||AD

So, EF||DC (Since, lines parallel to same line are parallel to one another)

Now, join A and C. And let AC intersect EF at point G.

Therefore, in triangle ADC,

EG|| DC

So, AE/ED = AG/GC (Since, lines drawn parallel to one side of triangle intersects the other two sides in distinct points. Then it divides the other two side in the same ratio)

Hence, Proved.