Question

Prove that the line segment joining the midpoints of a pair of opposite sides of a parallelogram

Answer 1

$\huge\underline\mathfrak{solution}$

Since, ABCD is a llgm

So, AB=CD and ABllDC

$</strong><strong>\</strong><strong>longrightarrow</strong><strong> \frac{1}{2}</strong><strong>AB</strong><strong> = \frac{1}{2} </strong><strong>DC</strong><strong> </strong><strong>$ and AEllDE

AE=DFand AEllDF

Therefore, Quadrilateral ABCD is a parallelogram.

Similarly, quadrilateral EBCF is also a parallelogram.

So, AEFD and EBCF are two parallelograms on the same base EF and between the same parallels AD and BC.

Therefore, ar(AEFD)=ar(EBCF)

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