Question

Give a definition for each of the following terms. Are there other terms that need to be defined first? What are they and how might you define them?
[i] Parallel lines
[ii] Perpendicular lines
[iii] Line segment
[iv] Radius of a circle
[v] Square

Answer 1

Hint: Definitions of some of the mathematical terms should be remembered. Recall the definitions of a line segment, a right angle and distance. Using these definitions define parallel lines, perpendicular lines, a line segment, the radius of a circle and a square.

Complete step-by-step answer:
[i] Parallel lines: Two lines in a plane are said to be parallel if they never intersect each other. Parallel lines can also be defined as the lines whose distance between each other does not change.
[ii] Perpendicular lines: Two lines are said to be perpendicular to each other if they intersect each other at right angles.
[iii] Line segment: A line segment can be defined as a line having two endpoints and a finite length.
[iv] Radius of a circle: A circle is a locus of a point which moves in a plane such that its distance from a fixed point is constant. The fixed point is known as the centre of the circle, and the fixed distance is known as the radius of the circle. In other words, the radius of the circle is the distance between a point on the circle and the centre of the circle.
[v] Square: A square is a quadrilateral with all sides equal and all angles equal. In other words, a square is a regular quadrilateral.
In order to define these terms, we need the definitions of a line, a quadrilateral, a right angle, distance and a circle.
The definitions of a line and a right angle are considered to be fundamental, and no specific definition is considered to be correct.
However, we can define a circle as a locus of a point which moves in a plane such that its distance from a fixed point is constant
We can define a quadrilateral as a closed figure consisting of only line segments with four sides.

Note: Many students forget to mention that parallel lines should be in a plane and write as the lines which never meet are parallel lines. This is incorrect since the skew lines never intersect each other as they are in parallel planes but are not parallel to each other.