What is the simplest proof of the pythagorean theorem you know? Maybe enough so to explain it to children.
I wouldn't call  this a proof, but it's a convincing argument good demonstration of what the theorem means, and I thought it was pretty cool. Hopefully should help with explaining it to kids, as you asked.
What I will say will be the worst in terms of beauty but you need to ask yourself what is a square triangle. How is it defined ?

Well, the answer is that 2 vectors are square when their scalar product is 0, which leads (after 1 or 2 lines) to the Pythagore Theorem

Edit :

Vectors are A and B ; C = A - B to "complete the triangle"
In the general case, ||C||2 = (A-B).(A-B) = ||A||2 + ||B||2 - 2 A.B
We see that ||C||2 = ||A||2 + ||B||2 if and only if A.B == 0 (i.e are square by definition of being square)