Step 1: Determine the relationship in the initial analogy pair: overlapping triangles relate to overlapping circles. The core change is the geometric shape, and consequently, the number of vertices, shifting from 3 (triangle) to \(\infty\) (circle).
Step 2: Apply this relationship to the next pair: overlapping squares. A square has 4 vertices. Following the established pattern of increasing vertices, the next shape is a pentagon (5 vertices). Therefore, the solution is a pair of overlapping pentagons, aligning with Figure 1.