Select the related geometrical term from the given alternatives: Line : Square :: Arc : ?

Introduction / Context:
This analogy uses basic geometry. A line and a square are related in a specific way, and you must find the geometric term that has a similar relationship with an arc. The question examines your understanding of how simple curves and straight segments relate to the complete two dimensional shapes they help to form.

Given Data / Assumptions:
- A line is a straight one dimensional figure that can be a side of a polygon such as a square.
- A square is a two dimensional plane figure bounded by four equal line segments at right angles.
- An arc is a curved segment that forms part of a circle.
- The missing term should be the two dimensional shape that an arc belongs to in the same way that a line belongs to a square.

Concept / Approach:
The pair Line : Square can be interpreted as "boundary element : complete figure." A square is bounded by line segments. Similarly, an arc is a curved boundary element of some closed curve. You need to identify the full figure for which an arc is a natural boundary component. Among the options Ring, Sphere, Circle, and Ball, we must choose the one whose boundary is formed by arcs.

Step-by-Step Solution:
Step 1: Understand the first pair. A line segment forms part of the boundary of a square. A square has four sides, and each side is a straight line segment. Step 2: Translate this into a pattern: "part of the boundary : entire two dimensional figure." Step 3: Now consider an arc. An arc is a portion of the circumference of a circle, that is, part of the boundary of a circular shape. Step 4: Check the options. A Ring is an annular region with two circular boundaries. A Sphere and a Ball are three dimensional, while the square is two dimensional in the first pair. Step 5: The simplest and direct counterpart is Circle, a two dimensional figure whose boundary is made of a continuous curve. An arc is simply a part of that circular boundary. Step 6: Therefore, Arc : Circle corresponds to Line : Square.

Verification / Alternative check:
Substitute each option into the relationship. Line : Square :: Arc : Ring is not parallel because a ring involves two concentric circles and is conceptually more complex than a square. Sphere and Ball introduce a shift from two dimensions to three dimensions, which breaks analogy symmetry. Only Circle keeps us within the same type of geometric context as a square, that is, simple plane figures bounded by one dimensional curves or segments.

Why Other Options Are Wrong:
Option A "Ring" denotes a shape with two circular boundaries and does not mirror the simple boundary to shape relation of a line and square.
Option B "Sphere" is a three dimensional surface in geometry and not a two dimensional figure like a square.
Option D "Ball" is also three dimensional, representing a solid sphere, so it does not maintain the dimensional consistency.

Common Pitfalls:
Learners sometimes get distracted by similar sounding words or by thinking of everyday objects rather than geometric definitions. Remember that in such reasoning questions, focusing on dimensionality and exact geometric roles of terms avoids confusion. Keeping track of whether we are dealing with lines, curves, surfaces, or solids is very important.

Final Answer:
The correct related geometrical term is Circle.