You can put this solution on YOUR website!
I'll give you a hint to get you started.
An equilateral polygon is simply a polygon with equal sides. So to prove that ABCD is equilateral, simply prove that the distance from A to B equals the distance from B to C. Then prove that the distance from B to C is equal to the distance from C to D. Finally prove that the distance from C to D is equal to the distance from D to A. In other words, show that
This will also show that AB=CD, CD=AB, etc (but this info is not needed)
Once you have done all of this, you can conclude that ABCD is equilateral since it has 4 equal sides.