Euclid Book I proposition 47 (The Pythagorean Theorem)

Drag Point B and C to make the triangle larger or smaller. Drag Point A to change where the right angle is.[br]Check the first checkbox and explain why those two triangles are congruent.[br]How does the fact that the triangles are congruent lead to the blue square having the same area as the blue rectangle?[br]Uncheck the first checkbox and check the second checkbox and explain why those two triangles are congruent.[br]How does the fact that the triangles are congruent lead to the red square having the same area as the red rectangle?[br]How does this prove the Pythagorean Theorem?