If E,F,G,H are the mid point …

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If E,F,G,H are the mid point of sides of parllelogram.show that ar(EFGH)=1÷2 ar(ABCD).

Posted by Sukhman Singh 4 years, 7 months ago

CBSE > Class 09 > Mathematics

1 answers

Meenal Khandelwal 4 years, 7 months ago

Const. Draw line he, ef, fg and gh Draw the line hf parallel to ab and de Such that ab is parallel to hf is parallel to de So abfh and defh are the parallelograms Now in parallelogram abfh Trialngle efh and parallelogram abfh are on the same base and between the same parallels. So triangle efh is 1/2 of parallelogram abfh (by mid point theo.)........~1 Similarly, area of triangle gfh= 1/2 area parallelogram edhf (mid point theo.)........~2 Now adding eqn.1 and 2 we get, Area ofParallelogram efgh=1/2 area of parallelogram abcd

1Thank You

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CBSE > Class 09 > Mathematics