1.

ABCD is a quadrilateral. E, F, G and H are the midpoints of AB, BC, CD and DA respectively. Prove that EFGH is a parallelogram.

Answer»

Given that E, F, G and H are the midpoints of the sides of quad. ABCD

In ΔABC; E, F are the midpoints of the sides AB and BC. 

∴ EF//AC and EF = 1/2 AC

Also in ΔACD; HG // AC

and HG = 1/2 AC

∴ EF // HG and EF = HG 

Now in □EFGH; EF = HG and EF // HG 

∴ □EFGH is a parallelogram.



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