If E, F, G and H are respectively the mid-points of the sides of a parallelogram ABCD, show that
.
Solution:
It is given that ABCD is a parallelogram. E, F, G and H are respectively the mid-points of the sides of a given parallelogram ABCD. Join GE.
We have
(Opposite sides of parallelogram are equal)
(1)
We also have
because
. (Opposite sides of parallelogram are equal) (2)
From (1) and (2), we can say that EBCG is a parallelogram.
(A quadrilateral is a parallelogram if one pair of opposite sides is equal and parallel.)
We can clearly see that
and parallelogram EBCG are on the same base and between same parallels.
(3)
Similarly, we have
(4)
Adding (3) and (4), we get
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