Mathematics
The Pythagorean Theorem
In any right triangle, the square of the hypotenuse equals the sum of squares of the two legs: a² + b² = c². It's the most-used result in geometry — from carpentry to coordinate geometry to relativity.
How to Approach The Pythagorean Theorem
Identify the right angle
Find the 90° corner. The side opposite that corner is the hypotenuse (c) — always the longest.
Label the two legs
The other two sides are the legs (a and b). Order doesn't matter — only which side is the hypotenuse.
Apply a² + b² = c²
Plug in any two known sides and solve for the third. For the hypotenuse: c = √(a² + b²). For a leg: a = √(c² - b²).
Frequently Asked Questions
Does the Pythagorean theorem work for any triangle?+
No, only for right triangles. For non-right triangles use the Law of Cosines: c² = a² + b² - 2ab·cos(C).
What are Pythagorean triples?+
Sets of three positive integers (a, b, c) that satisfy a² + b² = c². The simplest is (3, 4, 5); others include (5, 12, 13) and (8, 15, 17).
Can I use it on the SAT?+
Yes — the Pythagorean theorem appears on nearly every SAT math section, often disguised inside coordinate geometry or word problems.
Related Topics
More step-by-step guides in Mathematics and adjacent subjects.
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