1. **State the problem:** We have a 45°-45°-90° triangle with angles $m\angle ABC = 45^\circ$ and $m\angle ACB = 45^\circ$. We want to find the lengths of the legs $AB$, $AC$, and the hypotenuse $BC$. 2. **Recall the 45°-45°-90° triangle theorem:** In such a triangle, the legs are congruent, and the hypotenuse is $\sqrt{2}$ times the length of each leg. 3. **Set variables:** Let the length of each leg be $x$. Then: $$AB = AC = x$$ $$BC = x\sqrt{2}$$ 4. **Measure or assign values:** Since the problem does not provide specific lengths, the relationship is: - Legs: $AB = AC = x$ units - Hypotenuse: $BC = x\sqrt{2}$ units 5. **Summary:** The legs are equal, and the hypotenuse is $\sqrt{2}$ times a leg. This is the key property of a 45°-45°-90° triangle.