1. **Problem statement:** Given triangle RST with sides RS = 4, RT = 3, and ST = 5, show that triangle RST is a right triangle. 2. **Formula used:** To verify if a triangle is right-angled, use the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse (longest side), and $a$, $b$ are the other two sides. 3. **Identify sides:** Here, the longest side is $ST = 5$, so $c = 5$, and the other sides are $a = 4$, $b = 3$. 4. **Calculate squares:** $$4^2 + 3^2 = 16 + 9 = 25$$ 5. **Compare with hypotenuse square:** $$5^2 = 25$$ 6. **Conclusion:** Since $$4^2 + 3^2 = 5^2$$ triangle RST satisfies the Pythagorean theorem, so it is a right triangle. **Final answer:** Triangle RST is a right triangle because $4^2 + 3^2 = 5^2$.