Pythagorean Theorem
In a right triangle, the square of the hypotenuse equals the sum of squares of the other sides.
Also: hypotenuse theorem
Definition
The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides, expressed as a squared + b squared = c squared. It is one of the most fundamental results in Euclidean geometry. The theorem has hundreds of known proofs and has applications throughout mathematics, physics, and engineering.
Example
“A carpenter verifies that a wall is perfectly perpendicular to the floor by checking that a triangle with sides 3 feet, 4 feet, and 5 feet (a Pythagorean triple) fits in the corner, confirming a right angle.”
Synonyms
- right triangle theorem
- hypotenuse theorem
- a2+b2=c2
Images
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Related Terms
- Geometry
- Trigonometry
- Vector
- Distance Formula