The theorem
- In a right-angled triangle, a² + b² = c².
- c is the hypotenuse: the longest side, opposite the right angle.
Finding the hypotenuse
- Square the two shorter sides, add them, then square root.
- Sides 6 and 8: 36 + 64 = 100, so c = √100 = 10.
Finding a shorter side
- Square the hypotenuse and the known side, subtract, then square root.
- Hypotenuse 13, side 5: 169 − 25 = 144, so the side is 12.
Useful facts
- Pythagorean triples are whole-number sets such as 3, 4, 5; 5, 12, 13; and 8, 15, 17 (and multiples, like 6, 8, 10).
- To find the distance between two points, use the difference in x and the difference in y as the two shorter sides.
- If a² + b² = c² for a triangle's sides, the triangle is right-angled.
Key terms
- Hypotenuse
- The longest side of a right-angled triangle, opposite the right angle.
- Pythagoras' theorem
- In a right-angled triangle, a² + b² = c².
- Pythagorean triple
- Three whole numbers that fit a² + b² = c², such as 3, 4, 5.
- Square root
- The number that multiplies by itself to give a value: √144 = 12.