Sun March 18, 2012 By: Kimaya Patil

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

Expert Reply
Sun March 18, 2012
Let there  be a parallelogram ABCD with E,F mid points of sides AB and CD resp.
Now it can be seen that in both Quads AEFD and BEFC opposite sides are parallel so they also form a parallelogram .
Now , In Quad AEFD , we have area = AE * perpendicular distance between lines AE and DF
Similarly area BEFC  = BE * perpendicular distance between lines BE and CF
Now perpendicular distances between two parallel line always remains the same , Also AE = BE
So both the parallelograms are equal in area
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