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Question
In trapezium ABCD, sides AB and DC are parallel to each other. E is mid-point of AD and F is mid-point of BC.
Prove that: AB + DC = 2EF.
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Solution
Consider trapezium ABCD.
Given E and F are midpoints on sides AD and BC, respectively.
We know that AB = GH = IJ
From midpoint theorem,
EG = `1/2"DI", "HF" = 1/2`JC
Consider LHS,
AB + CD = AB + CJ + JI + ID = AB + 2HF + AB + 2EG
So, AB + CD = 2( AB + HF + EG ) = 2( EG + GH + HF ) = 2EF
AB + CD = 2EF
Hence Proved.
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