ABC is a right triangle with sides a, b, c as shown.[br][img]data:image/png;base64,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[/img]Click on the buttons, they will appear one by one.[br][img]data:image/png;base64,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[/img]Then you'll have a puzzle to complete using the three coloured triangles. [br][img]data:image/png;base64,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[/img]The triangles can be moved (drag and drop) or rotated using the round yellow handle at the right angles.[br][size=150][b]⛶ [/b][size=100]It's better to go full screen (click [b]⛶ [/b] at the bottom right) [/size][/size][br][br][i]When you get the final green check mark[/i] ✅ [i]answer the two questions below to prove the pythagorean theorem using this puzzle.[/i]

[color=#6aa84f][b][i]When you get the final green check mark[/i] ✅ [i]answer the two questions below to prove the pythagorean theorem using this puzzle.[/i][/b][/color]

We assume such a puzzle is always possible whatever right triangle ABC we start with. Check how the different lengths and angles fit perfectly together.

[b][size=150][color=#0000ff]Pythagorean theorem.[/color][/size][/b][br][b][color=#351c75][size=150] In any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs of the right triangle.[/size][/color][/b]