ABCD is a trapezium with AB || DC. E and F are points on non-parallel sides AD and BC respectively such that EF is parallel to AB. Show that`(A E)/(E D)=(B F)/(F C)`.

Explanation

To prove that \(\frac{AE}{ED} = \frac{BF}{FC}\) in trapezium \(ABCD\) where \(AB \parallel DC\) and \(EF \parallel AB\), we can follow these steps:

### Step 1: Identify the triangles
We have trapezium \(ABCD\) with \(AB \parallel DC\). Points \(E\) and \(F\) are located on sides \(AD\) and \(BC\) respectively, such that \(EF \parallel AB\).

### Step 2: Apply the Basic Proportionality Theorem
Since \(EF\) is parallel to \(AB\), by the Basic Proportionality Theorem (also known as Thales' theorem), we can conclude that:
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