show that the segment joining the midpoints of a pair of opposite sides of a parallelogram divide it into two equal parallelogram
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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)
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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