Pythagoras Variation Bithagoras, empirical discover (en)
A right triangle ABC is given with= 90°, along with a point X inside the triangle.
The perpendicular feet from X divide the sides a, b, c into a1, a2, b1, b2, and c1, c2.
Squares are constructed on these segments.
The areas of the squares on the legs are added together (blue), as are the areas of the
squares on the hypotenuse (violet).
Drag X and compare the sums of the areas. Can you find a general statement?
In which case does equality hold?
For which position of X do we obtain the well-known Pythagorean figure?