Glossary
Pythagorean theorem
In a right triangle, the squares of the two legs add to the square of the hypotenuse: a² + b² = c².
The Pythagorean theorem relates the three sides of a right triangle: the squares of the two shorter sides, the legs, add to the square of the longest side, the hypotenuse. Written as a² + b² = c², it lets you find any one side from the other two. With legs of 6 and 8, a² + b² = 36 + 64 = 100, and the hypotenuse is √100 = 10. To find a leg instead, subtract: given a hypotenuse of 17 and one leg of 8, b² = 289 − 64 = 225, so the other leg is 15. The name of the side matters: c is always the hypotenuse, the side across from the right angle and the longest of the three. The errors are adding the sides before squaring (6 + 8 = 14) and subtracting under the root when the hypotenuse was the unknown; the sum finds c, the difference finds a leg.
Taught in
Related terms
- quadratic formula — The quadratic formula solves any equation ax² + bx + c = 0: x = (−b ± √(b² − 4ac)) ÷ (2a).
- slope — The slope of a line is its steepness — the rise (vertical change) divided by the run (horizontal change), or the m in y = mx + b.
- circumference — The circumference is the distance around a circle: C = 2πr, where π is about 3.14 and r is the radius.
Source: OpenStax Prealgebra, Elementary Algebra and College Algebra, first editions (CC BY 4.0); NIST SP 811 (units). Each definition restates the two Mathematics guides in this exam, which carry the per-source citations on their own pages. (OpenStax 1e and NIST SP 811 accessed 2026-10-07)