Question

show that the line segment joining the mid-points of a pair of opposite sides of a parallelogram divide it into two equal parallelogram.

Answer 1

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Answer 2

 hi..
here is your answer..

In ||gm ABCD, E is the mid-point of AB and F is the mid-point of DC.  Also AB|| DC.

AB = DC and AB || DC

 ∴ (1/2)AB = (1/2)DC and AE || DF (Since E and F mid point of AB and DC)

∴ AE = (1/2)AB and DF = (1/2)DC

∴ AE = DF and AE || DF

∴Quadrilateral AEFD is a parallelogram Similarly, Quadrilateral EBCF is a parallelogram.

Now parallelogram AEFD and EBCF are on equal bases DF = FC and between two parallels AB and DC
∴ ar(||gm AEFD) = ar(||gm EBCF)
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