I'd be glad to help, but could you be a little more specific on what part of the proof is giving you trouble?

It'd be easier to help if we could talk in real time.  I don't suppose you have AIM?

-- Edited by Skifox at 18:09, 2007-04-05

The LUO main site has a messenger thing in the 'interactive' section that runs right in your browser. We could use that.

I hesitate to just plunk down a complete explanation. Walking you through it step by step and letting you figure out as much as possible would make you understand it better. I'll get started, though.

OK, I assume the diagram looks something like this:

This proof is all about areas, so let's start there.  What's the formula for the area of a trapezoid?

-- Edited by Skifox at 18:56, 2007-04-05

Close. It's ¹/₂(b₁ + b₂)h. You have two bases of different lengths on a trapezoid, so you use the sum of them.

When you plug in the variables from the diagram, you get ¹/₂(a + b)(a + b).  That simplifies to ¹/₂(a² + 2ab + b²).  Look familiar?  Just set it aside for now.

Now we go at the area a different way.  If you add together the areas of the three triangles it should give you the area of the trapezoid, right?  Go ahead and find those areas in terms of a, b, and c, add them up, and tell me what you get.