A villager Itwarri has a plot of land of the shape of a quadrilateral. The Gram Panchayat of the village decided to take over some portion of his plot from one of the corners to construct a Health Centre. Itwarri agrees to the above proposal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented

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Let ABCD be the quadrilateral plot. Produce BA to meet CD drawn parallel to CA at E. Join EC. Triangles EAC and ADC lie on the same line and between same  parallels DE and CA.Using the property mentioned above  ar(EAC)=ar(ADC)ar(ABCD)=ar(ABC)+ar(ACD)
=ar(ABC)+ar(ADC)
=ar(ABC)+ar(EAC)=ar(EBC)
 i.e., Quadrilateral ABCD=△EBC gives the explanation .

Question Text	A villager Itwarri has a plot of land of the shape of a quadrilateral. The Gram Panchayat of the village decided to take over some portion of his plot from one of the corners to construct a Health Centre. Itwarri agrees to the above proposal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented
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