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).
Correct Answer: A. Line, B. Circle
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