LINES AND ANGLES

LINES AND ANGLES
Point: A fine dot marked with a sharp edged pencil represents a point. It has no length, breadth and thickness. Points are denoted by capital letters like A,B,C etc., Geometrically a point is an undefined term.
Dimension of Point: A point has no dimensions point has no thickness or size, generally we should keep a dot as thin as possible to represent a point.
Example:  A person travelling along a straight path from Miyapur to Chintal, can be represented diagramatically as the first dot on the line named as point ‘T’ represnts Miyapur, the second dot ‘P’ represents a person and the third dot name as ‘H’ represents Chintal.

Line: Mark two points A and B on a plain white paper and join them with the help of a ruler and pencil you get the adjoint figure

This line segment AB is formed by joining the two points A and B. That means this has two end points.
    Observe the two adjacent figures: 

by extending the line, segment \(\overleftrightarrow {AB}\) on either side figure (ii) is formed . We read this \(\overleftrightarrow {AB}\) as “line AB” simply a line segment extended endlesly in both the directions is called a “line”. Some times a line is represented by a small letter l,m,n,....etc., 

Collinear Points: The points lying on the same line are called collinear points.
    Example: If  \(\overline {AB} \)= 3cm, \(\overline {BC} \)=4cm, the length of  must be 7cm  
    That means \(\overline {AB} +\overline {BC} =\overline {AC} \) , Therefore point ‘B’ must be in between A and C such points are called collinear points.
Note: 1) A Line has no end points 
    2) A line contains infinite number of points
    3) A line has length but no thickness.
    4) The line segment is a part of line
Example: Four points A,B,C, and D are marked on the following line 
     Here the points A,B,C,&D are lying on the same line or the line is passing through these points .Hence A,B,C, and D are called Collinear points.
Non-Collinear Points:   
    The points which do not lie on the same line are called Non-Collinear Points
 
 Note: Number of lines that can be draw through ‘n’ Non–Collinear points is \(\frac{{n\left( {n - 1} \right)}}{2}\)