If the side lengths of a triangle satisfy a² + b² = c², the triangle is a right triangle (the converse of the Pythagorean theorem).
📘 Example ①
Determine whether a triangle with sides 6, 8, and 10 is a right triangle.
Answer: 6² + 8² = 36 + 64 = 100 = 10². Since this is true, it is a right triangle.
Determine whether a triangle with sides 6, 8, and 10 is a right triangle.
Answer: 6² + 8² = 36 + 64 = 100 = 10². Since this is true, it is a right triangle.
📘 Example ②
Determine whether a triangle with sides 4, 5, and 7 is a right triangle.
Answer: 4² + 5² = 16 + 25 = 41 ≠ 49 = 7². Since this is not true, it is not a right triangle.
Determine whether a triangle with sides 4, 5, and 7 is a right triangle.
Answer: 4² + 5² = 16 + 25 = 41 ≠ 49 = 7². Since this is not true, it is not a right triangle.
💡 Key Point
- Let c be the longest side. If a² + b² = c², the triangle is a right triangle
- If the equation does not hold, the triangle is not a right triangle
Practice Problems
- Determine whether a triangle with sides 9, 12, and 15 is a right triangle.
Answers and Explanations
- Answer: A right triangle. 9²+12²=81+144=225=15².