Q8 of 8 Page 244

I draw any pentagon ABCDE and draw a triangle with equal area of it of which one vertex is C.

A. Draw the given pentagon ABCDE.



B. Draw the diagonal AC of pentagon ABCDE.


C. Draw a parallel line through point E to diagonal AC of pentagon ABCDE which intersects at F produced AB.


D. AC||FD, ΔABC is the required triangle.



Proof:


∆ACF = quadrilateral ACED (on same base AC and between same parallels AC and FD)


∴ ∆ACF = quadrilateral ACED


∆ABC + ∆ACF = quadrilateral ACED + ∆ABC (adding area of ∆ABC on both sides)


∴ ∆ABC = pentagon ABCDE


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