Does anyone know where I could find a book or resource of very simple intuitive proofs of the basic results in Geometry? I tutor geometry to middle schoolers, and find that due to shoddy mathematical education, they're not used to really rigorous step by step thinking. On the other hand, very intuitive proofs, like the ones from Lockhart's Lament they find very appealing.
If you haven't read Lockhart's Lament: http://www.maa.org/devlin/LockhartsLament.pdf
There's a proof for the area of a triangle that's given by inscribing the triangle in a rectangle. It's immediately obvious why the formula is the way it is that way. There's another nice proof of the theorem about inscribed angles in a circle.