# ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that

The figure is given below:

Given: ABCD is a trapezium
AB ll CD
Diagonals intersect at O
To Prove =

Construction:  Construct a line EF through point O, such that EF is parallel to CD.

Proof:

In ΔADC, EO is parallel to CD
According to basic propotionality theorem, if a side is drawn parallel to any side of the triangle then the corresponding sides formed are propotional

Now, using basic proportionality theorem in ΔABD and ΔADC, we obtain

In ΔABD, OE is parallel to AB

So, using basic proportionality theorem in ΔEOD and ΔABD, we get

From (i) and (ii), we get

Therefore by cross multiplying we get,

Hence, Proved

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