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

Asked by kimaya patil | 18th Mar, 2012, 01:47: PM

Expert Answer:

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

Answered by  | 18th Mar, 2012, 03:23: PM

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