Question

ABCD is a Quadrilateral E,F,G
and H are the mid points of the sides AB,BC, CD and DA respectively.
Prove that EFGH is a parallelogram.
Draw a rough figure and prove.​

Answer 1

Refer with the above attachments

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Answer 2

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Construction: Join BD(enclosed figure)

Now,

In ∆ABD, E and H are the midpoints of sides AB and AD respectively.

So,

➡EH||BD

➡EH=1/2 BD-----(1)--{By Midpoint theorem}

Also, in ∆BDC, F and G are the midpoints of sides BC and CD respectively.

➡FG||BD

➡FG=1/2 BD------(2)---{Midpoint theorem}

From (1) and (2), we get

↪EH=FG

↪EH||FG

One pair of opposite side of the quadrilateral is equal and parallel, therefore EFGH is a parallelogram.

Hence proved.