Show that line segment joining the mid points of a pair of opposite sides of a parallelogram, divides it into two equal parallelograms.

Asked by Topperlearning User | 17th Aug, 2017, 12:18: PM

Expert Answer:

Since ABCD is a parallelogram
AB = DC and AB  DC
AE = DF and AE  DF
Quadrilateral ABCD is a parallelogram.
Similarly, quadrilateral EBCF is also a parallelogram.
AEFD and EBCF are two parallelograms on the same base EF and between the same parallels, AD and BC.
ar(AEFD) = ar(EBCF)

Answered by  | 17th Aug, 2017, 02:18: PM