‘Lines are parallel if they do not intersect’ – is s...
‘Lines are parallel, if they do not intersect’ is the definition of parallel lines.
Euclid summarised these statements as definitions. He began his exposition by
listing 23 definitions in Book 1 of the ‘Elements’. A few of them are given below:
A point is that which has no part.
A line is breadth less length.
The ends of a line are points.
A straight line is a line which lies evenly with the points on itself.
A surface is that which has length and breadth only.
Lines are parallel, if they do not intersect.
The edges of a surface are lines.
A plane surface is a surface which lies evenly with the straight lines on
itself