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Question
ABCD is a quadrilateral in which AD = BC. E, F, G and H are the mid-points of AB, BD, CD and Ac respectively. Prove that EFGH is a rhombus.
Solution
Given that AD = BC …..(1)
From the figure,
For triangle ADC and triangle ABD
2GH = AD and 2EF = AD, therefore 2GH = 2EF = AD …..(2)
For triangle BCD and triangle ABC
2GF = BC and 2EH=BC, therefore 2GF= 2EH = BC …..(3)
From (1), (2) ,(3) we get,
2GH = 2EF = 2GF = 2EH
GH = EF = GF = EH
Therefore EFGH is a rhombus.
Hence proved.
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