Complete the analogy: “A : Square :: Arc : B”. Choose A and B so that each first term is a boundary part of the second (straight vs. curved).

Introduction / Context:This analogy checks geometric vocabulary. A square’s boundary comprises line segments (sides), whereas an arc is a curved segment of a circle’s circumference.

Given Data / Assumptions:

• Square boundary segments are straight lines.
• An arc is a part of a circle.
• We need the “part : whole (boundary)” relation consistently.

Concept / Approach:Maintain the same relationship type on both sides: boundary part to its enclosing figure. For the straight-edged polygon, use “line (side) : square”; for the curved figure, “arc : circle.”

Step-by-Step Solution:1) Identify a minimal boundary unit for a square: line.2) Identify the counterpart for a circle: arc.3) Map them as A : Square and Arc : B → A = Line, B = Circle.

Verification / Alternative check:“Perimeter/circumference” are total boundary lengths, not elemental parts; “line/arc” are correct granular parts.

Why Other Options Are Wrong:

• Perimeter/Circumference: Whole boundary measures, not parts.
• Line/Diameter: Diameter is a chord through center, not the whole circle.
• Rectangle/Chord: Mismatched figure/segment roles.
• Side/Sector: Sector is area region, not boundary unit.

Common Pitfalls:Confusing boundary measurements with boundary components.

Final Answer:A. Line, B. Circle