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Question

If A,B,C and D are any four points E and F are the middle points of AC and BD, respectively then prove that CB+CD+AD+AB=4EF.

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Solution

E is midpoint of AC
F i midpoint of BD
AB+AD=2AF(1)
CB+CD=2CF(2)
AB+AD+CB+CD=2(AF+CF)
AB+AD+CB+CD=2(FA+FC)
on adding (1) % (2) we get
AB+AD+CB+CD=2(2FE)
AB+AD+CB+CD=4EF
Hence proved


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