1. **State the problem:** We have a rectangle ABCD with AB = 8 and BC = 6. We need to find the lengths of AD, DC, and AC. 2. **Recall properties of a rectangle:** Opposite sides are equal and all angles are right angles. 3. **Find AD and DC:** Since ABCD is a rectangle, - AD = BC = 6 (opposite sides are equal) - DC = AB = 8 (opposite sides are equal) 4. **Find diagonal AC:** Use the Pythagorean theorem for right triangle ABC, $$AC = \sqrt{AB^2 + BC^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10$$ 5. **Final answers:** - $AD = 6$ - $DC = 8$ - $AC = 10$