A triangle has side lengths of 6, 8, and 10. Is it a right triangle? Explain.
Yes, it is a right triangle. We can use the Pythagorean theorem, which states that in any right triangle, the sum of the squares of the lengths of the legs (the sides adjacent to the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).
In this case, 6² + 8² = 36 + 64 = 100, and 10² = 100, so the equation is true:
6² + 8² = 10²
Therefore, the triangle satisfies the Pythagorean theorem and is a right triangle.