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In Figure, A B C D E\ is a pentagon. A ...

In Figure, `A B C D E\ ` is a pentagon. A line through `B` parallel to `A C` meets `D C` produced at `Fdot` Show that: `a r\ ( A C B)=a r\ ( A C F)` `a r\ (A E D F)=a r\ (A B C D E)`

Text Solution

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Join AF.
`triangleACB and triangleACF` have the same base AC and lie between the same parallels AC and BF.
`therefore ar(triangleACB)=ar(triangleACF)`.
And so, `ar(triangleACB)+ar(triangleACDF)=ar(triangleACF)+ar(triangleACDE)`
`rArr ar(ABCDE)=ar(AEDF)`.
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