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
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(i) Parallel lines : Two straight lines which have no point in common are said to be parallel to each other. ‘Point’ and ‘straight line’ will have to be defined first. ‘Point’ and ‘straight line’ as defined in Euclid’s text are : 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.
(ii) Perpendicular lines : If one among two parallel lines is turned by 90°, the two lines become perpendicular to each other. Parallel lines has been defined before, ‘rotation through 90° needs further defining. Rotation may be assumed as an intuition therefore, can not be used.
(iii) Line segment : A line with two end points is a line segment. ‘Line’ and ‘point’ have been defined before.
(iv) Radius of a circle : The line segment with one end point at the centre and the other at any point on 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.
(v) 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
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