Quick Triangle Sum & Pythagorean Proof

Just a quick, pretty unoriginal sketch to help secondary/tertiary students think through the justification for the sum of the angles in a triangle.

As a dynamic webpage or the original geogebra file.

EDIT:  As my students investigated (see these sketches elsewhere), they got interested in proofs of the Pythagorean Theorem.  Since they were investigating so nicely on their own, with interesting results, I had time to draw up a familiar proof in Geogebra.  Webpage or geogebra file.  The webpage has some additional hints to help towards a proof.