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if abcd is a quadrilateral and e & f are midpoint of ac & bd respectively. prove that ab+ac+cb+cd = 4ef

if abcd is a quadrilateral and e & f are midpoint of ac & bd respectively. prove that ab+ac+cb+cd = 4ef

Grade:12th pass

1 Answers

Satyajit Samal
askIITians Faculty 34 Points
9 years ago
The correct question isAB+AD+CB+CD=4EF
Since F is the midpoint of BD, we getAB+AD = 2AF…...(1)
Similarly CB+CD = 2 CF…....(2)
Adding (1) and (2) we getAB+AD+CB+CD=2\left ( AF+CF \right ) \\ \Rightarrow AB+AD+CB+CD = -2\left ( FA+FC \right ) \\ \Rightarrow AB+AD+CB+CD = -2 \left ( 2FE \right ) \\ \RIghtarrow AB+AD+CB+CD = 4EF
Hence proved.

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