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In the figure, ABCD is a quadrilateral. ...

In the figure, ABCD is a quadrilateral. A line DP drawn parallel to diagonal AC from point D, meet BC produced at P. Prove that:
are of `Delta ABP = " area of " square ABCD`

Text Solution

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Here `AC|\ |DP` (given)
`DeltaACP` and `DeltaACD` are on same base AC and between the same parallel lines AC and DP.
`therefore` area of `DeltaACP=` area of `squareABCD`
Adding area of `Delta ABC` on both sides.
area of `DeltaACP+` area of `DeltaABC=` area of `DeltaACD+` area of `DeltaABC`
`rArr` area of `DeltaABP=` area of `square ABCD`.
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