Q. 94.4( 241 Votes )
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.
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,
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