Q.2. 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

Solution:

  1. Parallel lines: Two straight lines which do not meet; that is, two lines in a plane that do not intersect or do not have any point in common, are said to be parallel.

    ‘Point’, ‘straight line’ and ‘plane’ will have to be defined first. ‘Point’ and ‘straight line’ as defined by Euclid,

    A point is that which has no part.

    A line is breadthless length and a straight line is a line which lies evenly with the points on itself.

    A plane surface is a surface which lies evenly with the straight lines on itself.


  2. Perpendicular lines: A line is said to be perpendicular to another line if the two lines intersect at a right angle.

    Right angle is an undefined term here. An angle of 90o is called right angle.


  3. Line segment: A line with two end points is a line segment.

    ‘Line’ and ‘point’ have been defined before.


  4. Radius of a circle: The line segment joining the centre of the circle with any point on the circle is called radius of the circle.

    ‘Centre’ may be defined (assuming inside) as a point inside the circle which is at the same distance from all points on the circle.


  5. Square: A quadrilateral with all sides equal and all angles right angles is a square.

    A quadrilateral is a figure with four sides. ‘Figure’, ‘side’ and ‘angle’ may be assumed known.