In any right triangle, the square of the hypotenuse equals the sum of the squares of the two legs. This single theorem connects algebra and geometry.
For a right triangle with legs a and b and hypotenuse c: a² + b² = c². The hypotenuse is always opposite the right angle and is the longest side.
If a=3 and b=4: c² = 9 + 16 = 25, so c = 5. The 3-4-5 right triangle is the most famous Pythagorean triple.
If c=13 and a=5: b² = 169 - 25 = 144, so b = 12. Rearrange: b² = c² - a².
Sets of whole numbers satisfying a²+b²=c²: (3,4,5), (5,12,13), (8,15,17), (7,24,25), and any multiples of these.
Q1: A right triangle has legs 5 and 12. What is the hypotenuse?
Q2: A right triangle has hypotenuse 10 and one leg 6. The other leg is:
Q3: Which set is a Pythagorean triple?