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.
Narrated · 16:9 · every frame verified for overlaps, spacing and edges before rendering
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
