# Thread: [SOLVED] Midsegment of Trapezoid

1. ## [SOLVED] Midsegment of Trapezoid

2. Are AB and CD equal?

3. Let $AC\cap BD=O$ and $MN\perp BC, \ M\in AD, \ N\in BC, \ O\in MN$

Then $DH=MN$ and $MO=\frac{AD}{2}, \ ON=\frac{BC}{2}$

$\Rightarrow MN=MO+ON=\frac{AD+BC}{2}=EF$

4. ## Help!

I don't understand this. Please give me a simple prove.

5. See attachment.

6. Thanks a lot!

I also spent sometime thinking about this problem again and found an another way of solving.

Triangle BDG is a right isosceles triangle. ADGC is a parallelogram.