Why a² + b² = c²: rearrange four triangles
Two identical large squares each contain four congruent right triangles arranged differently. In one square the leftover space forms a single tilted square of side c; in the other, two smaller squares of sides a and b. Since both big squares have equal area and the triangles match, the leftover areas must be equal, giving c² = a² + b². Useful for students meeting the Pythagorean theorem through a visual, proof-without-words approach.
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The prompt that made it
Two copies of the same big square, each holding four identical right triangles. Arranged one way the leftover space is a tilted square of side c. Arranged the other way the leftover space is two squares, of sides a and b. Same leftover area, so c² = a² + b².
Make the next one in this series
- Show an animated algebraic proof of the Pythagorean theorem using area expansion (a+b)²
- Demonstrate the converse of the Pythagorean theorem with a right triangle test
- Animate a 3D extension showing the theorem applied to space diagonals of a box
