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in Parallelograms by (65.5k points)

If E, F, G and H are respectively the mid-points of the sides of a parallelogram ABCD, show that

ar(EFGH) = \(\frac{1}{2}\)ar(ABCD)

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Data: E, F, G and H are mid-points of the sides of a parallelogram ABCD, 

To Prove: area (EFGH) = \(\frac{1}{2}\)area (ABCD) 

Construction: HF is joined. 

Proof: 

Now, AD = BC and AD || BC 

∴ 2AH = 2BF 

∴ AH = BF and AH || BF 

∴ AHFB is a parallelogram. 

Similarly, HDCF is a parallelogram. 

Now, DEHF and Quadrilateral AHFD are on base HF and in between HF || AB.

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