In the given figure , $A B C D$ is a quadrilateral.A line through $D$ parallel to $A C$ meets $B C$ produced at $E$ .Prove that ar $(△ A B E) =$ area of quadrilateral $A B C D$

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Solution

From the figure, notice that $△ A D C$ and $△ A C P$ are on the same base between the same parallel lines.
Hence ar $(△ A D C) =$ ar $(△ A C E)$
Also,area of quadrilateral $A B C D =$ ar $(△ A D C) +$ ar $(△ A B C)$
$=$ ar $(△ A C P) +$ ar $(△ A B C)$
$=$ ar $(△ A B E)$

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