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: We give definition of each of the given terms and check if we require any other definition to define the given terms.

Complete step-by-step solution:
(i) Parallel lines
Definition: Two lines are said to be parallel to each other if they never meet (intersect) with each other.
* The distance between the lines always remains the same.
* Parallel lines help in understanding relationship between paths of object and sides of shapes (Example: rectangle has opposite sides parallel and equal, parallelogram has opposite sides parallel)
* Examples: Zebra crossing on the road, Rail tracks etc.
* Lines AB and CD are parallel on a plane surface.
* Denoted by pair of vertical lines ( \[\parallel \])\[AB\parallel CD\]

(ii) Perpendicular lines
Two lines are said to be perpendicular to each other if they intersect each other at a right angle i.e.\[{90^ \circ }\].
* Perpendicular lines and properties of triangles help to calculate heights and distances.
* Examples: Street corner, Red Cross symbol etc.
* Lines AB and CD are perpendicular to each other.
* Denoted by (\[ \bot \]) \[AB \bot CD\]

(iii) Line segment
 A line joining two points is said to be a line segment when it has definite end points.
* It cannot be extended.
* It has definite length.
* Examples: Rod of fixed length, pen etc.
* A line segment is usually denoted as \[\mathop {AB}\limits^{\_\_\_\_\_} \]

 (iv) Radius of a circle
Radius of a circle is defined as the distance from center of the circle to any point on the circle.
* It is the distance from center O to any point on circumference.
* Radius helps in calculation of diameter, circumference and area.
* OA is the radius of the circle.

(iv) Square
A quadrilateral is called a square if it has all its four sides of equal length and each angle equal to the right angle.
* Opposite sides of the square are parallel.
* It falls under category of a quadrilateral, polygon, rhombus and rectangle
* Two diagonals bisect each other at right angle.
* ABCD is a square with sides \[AB = BC = CD = DA\] and all angles \[\angle A = \angle B = \angle C = \angle D = {90^ \circ }\]
* Examples: Chessboard, square windows etc.

For defining these terms, student should have knowledge about the following:
1) Point: A point is an exact position on a plane surface. It is usually denoted by capital single letters (say ‘X’).
2) Line: A line is the shortest distance between two points.
3) Surface: A portion of space having length and breadth but no thickness.
4) Angle: An angle is defined as a figure that is formed at the place where two lines meet. It is measured in degree or radian.

Note: Students many times get confused with the definition of line and line segment, keep in mind line segment is a fixed part of a line where the line has infinite length and line segment has finite length. Confusion occurs as we sometimes write line AB and students assume the points A and B are fixed but always check if we are given a line or a line segment.