☼ Undefined  Terms  :  In geometry there are four undefined terms, namely a point, a line, a plane and a space.

But there is a certain relation in above four words given as below :

Point     Line       Plane      Space.

■ Line  :  Line is partially defined by following two postulates  :

Postulate  – 1  :–     Every line has at least two distinct points.

Postulate  – 1  :–     Two distinct points lie on a unique ( one and only one ) line.

 Note  :  (i) Lines are denoted by letters  l, m, n  or  l₁, l₂, l₃ etc.

(ii) An infinite no. of  lines passes through one and only one point.

 ■ Collinear  Points  :    Points lying on the same line are called collinear points. Otherwise they are called non–collinear points.

 Note  : If  all the points are lying on the same line, they are called collinear points.

■ Distance Postulate  :   With each pair of  points, there is associated one and only one non–negative real number, called the distance between these points. The distance between points P and Q is denoted by  d(P, Q)   or   PQ   or

 Properties  :

(i) For  Points  P, Q ;    PQ     0

(ii) PQ  =  0  if   and  only  if   P  =  Q.

(iii) For  Points  P, Q,    PQ   =   QP

(iv) For  Points  P, Q, R ;     PQ  +  QR    PR

   Note  :

(i) If   A(a)  and  B(b),  then  AB  =

(ii) If   A(x₁, y₁)  and  B(x₂, y₂),  then  AB  =

■ Line – Segment  :   The set of  all points of   lying between A  and  B together with A and B is called a line–segment. And is denoted by .

Note  : 

(i)   =  { A, B }  { P /  A – P – B,  P   }

(ii) Line–segments having equal lengths are called congruent line–segment.

(iii) If  M is the mid–point of   ,  then

• M lies between A and B, that is, A – M – B.
• M is equidistant from A and B, that is AM  =

  (iv) Every line–segment has one and only one mid–point.

  (v) If   A(a)  and  B(b),  then  mid–point of    is  m  =

  (vi) If   A(x₁, y₁)  and  B(x₂, y₂),  then  mid–point of    is

m  =

 ■ Ray  :   The set of  point A and all the points on the side of  A towards B on the line   is called a ray AB. The ray AB is denoted by .

Note  :  

(i)  =      { P /  A – B – P,  P  }

(ii) If   C  ,  then   and    are equal rays.  i.e.    =  

(iii) Two distinct rays in the same line and having the same initial points are called rays opposite to each other or opposite rays.

e.g.     &     are  opposite  rays.

(iv) A line-segment or a ray or a line passing through the midpoint of  a line-segment AB is called a bisector of   .

• A bisector of a line-segment can be a line-segment or a ray  or a
• A bisector of  a line-segment  intersects it in the mid-point of  .

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