Rearrangement proofs
In one rearrangement proof, two squares are used whose sides have a measure of $${\displaystyle a+b}$$ and which contain four right triangles whose sides are a, b and c, with the … See more

The converse of the theorem is also true:
Given a triangle with sides of length a, b, and c, if a + b = c , then the angle between sides a and b is a right angle.
For any three positive real numbers a, b, and c such that a + b = c , there exists a triangle with sides … See more

Similar figures on the three sides
The Pythagorean theorem generalizes beyond the areas of squares on the three sides to any See more

• Mathematics portal
• Addition in quadrature
• At Dulcarnon
• British flag theorem
• Bride's Chair
• Fermat's Last Theorem See more

This theorem may have more known proofs than any other (the law of quadratic reciprocity being another contender for that distinction); the … See more

Pythagorean triples
A Pythagorean triple has three positive integers a, b, and c, such that a + b = c . In other words, a … See more

There is debate whether the Pythagorean theorem was discovered once, or many times in many places, and the date of first discovery is uncertain, as is the date of the first proof. Historians of See more