This is an important theorem that holds for the three sides of a right triangle.
Pythagorean Theorem
In a right triangle, let the two legs forming the right angle be a and b, and let the hypotenuse be c:
a² + b² = c²
📘 Example ①
In a right triangle, find the hypotenuse when the two legs are 3cm and 4cm.
Answer: c² = 3² + 4² = 9 + 16 = 25. c = 5cm
In a right triangle, find the hypotenuse when the two legs are 3cm and 4cm.
Answer: c² = 3² + 4² = 9 + 16 = 25. c = 5cm
📘 Example ②
Find the other leg of a right triangle whose hypotenuse is 13cm and whose one leg is 5cm.
Answer: b² = 13² - 5² = 169 - 25 = 144. b = 12cm
Find the other leg of a right triangle whose hypotenuse is 13cm and whose one leg is 5cm.
Answer: b² = 13² - 5² = 169 - 25 = 144. b = 12cm
💡 Key Point
- a² + b² = c² (c is the hypotenuse)
- To find the third side from two sides, use a square root
- Famous integer ratios: 3:4:5, 5:12:13, 8:15:17
Practice Problems
- Find the hypotenuse when two sides of a right triangle are 5cm and 12cm.
- Find the other leg of a right triangle whose hypotenuse is 10cm and whose one leg is 6cm.
Answers and Explanations
- Answer: 13cm. 5²+12²=25+144=169=13².
- Answer: 8cm. 10²-6²=100-36=64=8².