Analogy — Circle : Arc :: Square : ?

Introduction / Context:
We match a whole geometric figure to a characteristic part. An arc is a proper part of a circle. We must find the analogous part of a square from the options provided.

Given Data / Assumptions:

• Circle → arc (a portion of its boundary).
• Square → ? (a proper part associated with its boundary).
• Options include shapes (triangle, sphere, rectangle) and primitive elements (line, diagonal).

Concept / Approach:
The boundary of a square is composed of straight line segments (sides). By parallel, “arc” is to “circle” as “line (segment)” is to “square”. Among the given choices, “Line” best captures the boundary-part relation.

Step-by-Step Solution:

Verification / Alternative check:
Squares have four line segments as sides; “diagonal” is an interior segment, not a boundary part.

Why Other Options Are Wrong:

• Triangle/Rectangle/Sphere: wholes, not parts; wrong level.
• Diagonal: interior segment; not perimeter like an arc is for circle.

Common Pitfalls:
Selecting “diagonal” due to familiarity; it breaks the perimeter-part parallelism.

Final Answer:
Line