1. **Problem:** Find the missing side lengths of a right triangle with a 45° angle, hypotenuse 6, opposite side $v$, adjacent side $u$. 2. **Formula:** In a 45°-45°-90° triangle, the sides are in the ratio $1:1:\sqrt{2}$, where the legs are equal and the hypotenuse is $\sqrt{2}$ times a leg. 3. **Step:** Let each leg be $x$. Then hypotenuse $= x\sqrt{2} = 6$. 4. **Solve for $x$:** $$x = \frac{6}{\sqrt{2}}$$ 5. **Simplify by rationalizing the denominator:** $$x = \frac{6}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{6\sqrt{2}}{\cancel{\sqrt{2}}\cancel{\sqrt{2}}} = 3\sqrt{2}$$ 6. **Answer:** Both legs $u$ and $v$ are equal to $3\sqrt{2}$. **Final result:** $$u = v = 3\sqrt{2}$$