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Any line parallel to the parallel sides ...

Any line parallel to the parallel sides of a trapezium divides the non-parallel sides proportionally.

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A trapezim ABCD in which AB||DC.
Also a line EF||AB||DC.
To prove , ` (AE)/(ED) = ( BF)/(FC)`
Also in ` DeltaBDC,` since GF||DC
`(BF)/(FC) = (BG)/(GD)` ( by B.P theorem)
From (1) and (2) ,we have
` (AE)/(ED) = (BF)/(FC)` Hecne proved
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