1. **State the problem:** We are given a triangle ABC with side lengths $AB=6$ cm, $AC=8$ cm, and $BC=10$ cm. We need to determine if triangle ABC is a right triangle. 2. **Recall the Pythagorean theorem:** A triangle is right-angled if the square of the longest side equals the sum of the squares of the other two sides. 3. **Calculate the squares of the sides:** - $AB^2 = 6^2 = 36$ - $AC^2 = 8^2 = 64$ - $BC^2 = 10^2 = 100$ 4. **Check the Pythagorean condition:** - $AB^2 + AC^2 = 36 + 64 = 100$ - Since $AB^2 + AC^2 = BC^2$, the triangle satisfies the Pythagorean theorem. 5. **Conclusion:** Therefore, triangle ABC is a right triangle.