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.

Answer 1

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.