Proof of Pythagoras’ Theorem

Yeung Lai In

This video demonstrates how to prove the Pythagoras’ theorem without words. Pythagoras’ theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.” The teacher uses the free educational software (GeoGebra) to display the proof as self-evident by a dynamic, geometric diagram without any accompanying explanatory text. The diagram consists of two squares with sides of length a+b, and both have the same area. The purple region in each square consists of four abc right-angled triangles in two different arrangements, and so both purple regions have the same area. The Pythagoras’ theorem follows automatically that the remaining yellow regions in the two squares have equal areas by comparison. This pictorial explanation is clever and pretty and lets students appreciate how slick mathematics can genuinely be.

Video Information
Category | Online teaching Language | Cantonese
Level | Subject | Mathematics

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