Analogy — “Triangle : Hexagon”. Select the pair that preserves the sides-doubling pattern (3 → 6 corresponds to 4 → 8).

Introduction / Context:Polygons are classified by the number of sides. A triangle has 3 sides; a hexagon has 6 sides—double the number. We must find a pair that mirrors this doubling from another starting polygon.

Given Data / Assumptions:

• 3 → 6 implies “sides × 2.”
• Choose a pair where first polygon’s sides doubled equals the second polygon’s sides.

Concept / Approach:Rectangles have 4 sides; octagons have 8 sides. Thus 4 → 8 mirrors 3 → 6. Other options either involve 3D shapes, unrelated categories, or do not follow the doubling rule.

Step-by-Step Solution:

Verification / Alternative check:This interpretation is standard in quantitative analogies of geometric figures.

Why Other Options Are Wrong:They either mismatch dimensionality (cone/sphere), do not double (pentagon→heptagon is +2), or are category leaps (angle vs quadrilateral).

Common Pitfalls:Confusing additive patterns (+n) with multiplicative patterns (×2) when the stem clearly suggests doubling.

Final Answer:Rectangle : Octagon