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In Figure, A B C D is a quadrilateral an...

In Figure, `A B C D` is a quadrilateral and `B E_|_A C` and also `B E` meets `D C` produced at `E` , Show that area of ` A D E` is equal to the area of the quadrilateral `A B C Ddot`

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`/_\ABC and /_\EAC`
`"Are on same base AC and between same parallels" `
`therefore "AC is parallel to BC"`
`therefore ar(/_\ABC)=ar(EAC)`
`=>"Adding ar"(/_\ADC)" to both sides" `
`ar(/_\ABC)+ar(/_\ADC)=ar(/_\ECA)+ar(/_\ADC)`
`ar(Quadrilateral ABCD)=ar(/_\ADE)`
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