1. **State the problem:** We have two circles: one centered at point A with radius equal to the length of segment AB, and another centered at point C with the same radius AB. These circles intersect at two points, and one intersection point is labeled D. 2. **What to find:** Compare the lengths of segments AD and CD. 3. **Formula and reasoning:** The radius of a circle is the distance from its center to any point on the circle. Since D lies on the circle centered at A with radius AB, the length of AD equals AB. Similarly, since D lies on the circle centered at C with radius AB, the length of CD also equals AB. 4. **Intermediate work:** Since both circles have radius AB, we have: $$AD = AB$$ $$CD = AB$$ 5. **Conclusion:** Therefore, the lengths of segments AD and CD are equal: $$AD = CD$$ This is because point D lies on both circles, so it is exactly the same distance from A and from C, equal to the radius AB.