1. **State the problem:** We need to determine which triangles with given side lengths are right triangles. 2. **Formula used:** For a triangle with sides $a$, $b$, and $c$ (where $c$ is the longest side), the triangle is right-angled if it satisfies the Pythagorean theorem: $$a^2 + b^2 = c^2$$ 3. **Check Triangle 1:** Sides are 4, 6, 10. Longest side is 10. $$4^2 + 6^2 = 16 + 36 = 52$$ $$10^2 = 100$$ Since $52 \neq 100$, Triangle 1 is not a right triangle. 4. **Check Triangle 2:** Sides are 6, 8, 10. Longest side is 10. $$6^2 + 8^2 = 36 + 64 = 100$$ $$10^2 = 100$$ Since $100 = 100$, Triangle 2 is a right triangle. 5. **Check Triangle 3:** Sides are 10, 24, 26. Longest side is 26. $$10^2 + 24^2 = 100 + 576 = 676$$ $$26^2 = 676$$ Since $676 = 676$, Triangle 3 is a right triangle. **Final answer:** Triangles 2 and 3 are right triangles. Therefore, the correct choice is **C. Triangle 2 and triangle 3 are right triangles.**