Just click on the Green Flag. Press SPACE to cycle through the proof (no numerics). The Pythagorean Theorem is generalized to any 'similar' shapes constructed on the three sides of any right triangle. The similar shapes have the property that the sum of the areas of the similar figures constructed on the smaller sides equals the area of the similar figure constructed on the hypotenuse!
Credit for idea to Mathologer on You Tube. See video: Visualising Pythagoras: ultimate proofs and crazy contortions https://www.youtube.com/watch?v=p-0SOWbzUYI&t=1100s As I watched Mathologer's Pythagoras video (see above) I was thunderstruck by the 'simplest proof' he gives for the Pythagorean Theorem. He said, construct the altitude from the 90º angle to the hypotenuse and, as he says, "wait for it! There it is!" I've been a mathematics teacher since 1964 and I had never seen this proof. So, I had to share the proof with the Scratch community. Besides being simple (no numerics needed), it is an elegant use of mirror symmetry. The coordinates of the orange trianglel are A: (-40,60), B: (-40,0), C: (40,0). The Pythagorean theorem and similar triangles are used to compute the coordinates of point D reflected across the y-axis, point D across the x-axis, and point B across the hypotenuse. A big thank you to the following for their very helpful 'triangle fill' projects: JudasR Let's Fill a Triangle project https://scratch.mit.edu/projects/18849911/ I used the code from this project. tbpatj Triangle Filling Tutorial project https://scratch.mit.edu/projects/65142508/ A very helpful tutorial. See https://scratch.mit.edu/projects/2760223/ by dapontesgr for another generalized proof.
