Pythagorean Theorem
In a right triangle, a² + b² = c² relates the two legs to the hypotenuse.
This is a free explanation of Pythagorean Theorem — a preview, not the full interactive lesson. The lesson, practice, quizzes, and AI Tutor are inside the app.
In a right triangle, the square of the hypotenuse (side c — the longest side, always opposite the right angle) equals the sum of the squares of the two legs (a and b): a² + b² = c². The first step in any Pythagorean problem is to identify the hypotenuse — it is always opposite the right-angle box and always the longest side.
To find the hypotenuse, use c = √(a² + b²). To find a missing leg instead, rearrange to a = √(c² − b²). Square the known sides, add or subtract as the formula requires, then take the square root.
Some combinations appear so often they are worth recognizing instantly: the Pythagorean triples 3-4-5, 5-12-13, and their multiples (6-8-10, 9-12-15). If a problem shows legs of 3 and 4, the hypotenuse is automatically 5. The theorem applies only to right triangles.
Worked example
A right triangle has legs of 6 and 8. Find the hypotenuse.
- Identify the hypotenuse: c is opposite the right angle — that is what we are solving for.
- Write the theorem and substitute: 6² + 8² = c².
- Square the legs and add: 36 + 64 = 100, so c² = 100.
- Take the square root: c = √100 = 10.
c = 10 (the 6-8-10 triple, double the 3-4-5)
On the test: The GED & HiSET frequently use the 3-4-5 and 5-12-13 triples, including a ladder leaning against a wall.
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