Textbook: Basic Concepts in Geometry | Mathematics Class 6 (Maharashtra Board) PDF Download

 Page 1


1
B
1
PART ONE
Basic Concepts in Geometry 
A
B
A
        Points
 A point is shown by a tiny dot. We can use a 
pen or a sharp pencil to make the dot. The dots in 
the rangoli are the symbols for points. 
 A point can be given a name. Capital letters of 
the alphabet are used to name a point. The points 
P, A and T are shown in the figure alongside.
Line Segments and Lines
 Take two points A and B on a sheet of paper 
and join them using a ruler. We get the straight line 
AB. Can we extend this line further on the side of          
point B? On the side of point A? How far can we 
extend it?
 We can extend the line in both directions till the 
edges of the paper. If the paper is very big, the line 
can be very long, too. 
How long would the line be on a playing field?
Let’s discuss. 
  Complete the rangoli. Then, have a class  
discussion with the help of the following questions :
(1) What kind of surface do you need for making
a rangoli?
(2) How do you start making a rangoli?
(3) What did you do in order to complete the
rangoli?
(4) Name the different shapes you see in the
rangoli.
(5)	 Would it be possible to make a rangoli on a
scooter or on an elephant’s back?
(6)	 When making a rangoli on paper, what do you
use to make the dots?
Let’s learn.
A
P
T
?? ?? ??
Page 2


1
B
1
PART ONE
Basic Concepts in Geometry 
A
B
A
        Points
 A point is shown by a tiny dot. We can use a 
pen or a sharp pencil to make the dot. The dots in 
the rangoli are the symbols for points. 
 A point can be given a name. Capital letters of 
the alphabet are used to name a point. The points 
P, A and T are shown in the figure alongside.
Line Segments and Lines
 Take two points A and B on a sheet of paper 
and join them using a ruler. We get the straight line 
AB. Can we extend this line further on the side of          
point B? On the side of point A? How far can we 
extend it?
 We can extend the line in both directions till the 
edges of the paper. If the paper is very big, the line 
can be very long, too. 
How long would the line be on a playing field?
Let’s discuss. 
  Complete the rangoli. Then, have a class  
discussion with the help of the following questions :
(1) What kind of surface do you need for making
a rangoli?
(2) How do you start making a rangoli?
(3) What did you do in order to complete the
rangoli?
(4) Name the different shapes you see in the
rangoli.
(5)	 Would it be possible to make a rangoli on a
scooter or on an elephant’s back?
(6)	 When making a rangoli on paper, what do you
use to make the dots?
Let’s learn.
A
P
T
?? ?? ?? 2
 Look at the pictures. What do you see? 
Rays starting from the sun go forward in all 
directions. Light rays from the torch also 
start from a point and go forward 
continuously in one direction. 
P
Q
 A ray is a part of a line. It starts at one point and goes 
forward continuously in the same direction. The starting point 
of a ray is called its origin. Here, P is the origin. An arrowhead is drawn to show that the 
ray is infinite in the direction of Q. The figure can be read as ray PQ. 
The ray PQ is not read as ray QP.
 Let’s imagine that we can extend this line forever 
without any limits on both sides. To show this extended 
line on paper, we use arrowheads at both ends of the 
line. In mathematics, when we say line, we mean ‘straight 
line’. The first line that we drew was only from point A 
to point B. It was a piece or a segment of the longer line. 
A line segment has two points showing its limits. They 
are  called  endpoints.  We  write  line  segment  AB  as 
‘seg AB’ in short. A and B are its endpoints. A line is 
named using a small letter or by using any two points on 
the line. Line l has been shown alongside. Its name can 
also be written as line PQ or line QP. 
Rays
A
B
P Q
Activity 1 : Draw a point on the blackboard. Every student now 
draws a line that passes through that point. 
How many such lines can be drawn? 
Activity 2 : Draw a point on a paper and use your ruler to draw lines 
that pass through it. How many such lines can you draw?
An infinite number of lines can be drawn through one point. 
 When two or more lines pass through the same point, they are called concurrent 
lines and the common point through which they pass is called their point of concurrence. 
In the figure alongside, which is the point of concurrence? Name it.
Try this.
P
l
Page 3


1
B
1
PART ONE
Basic Concepts in Geometry 
A
B
A
        Points
 A point is shown by a tiny dot. We can use a 
pen or a sharp pencil to make the dot. The dots in 
the rangoli are the symbols for points. 
 A point can be given a name. Capital letters of 
the alphabet are used to name a point. The points 
P, A and T are shown in the figure alongside.
Line Segments and Lines
 Take two points A and B on a sheet of paper 
and join them using a ruler. We get the straight line 
AB. Can we extend this line further on the side of          
point B? On the side of point A? How far can we 
extend it?
 We can extend the line in both directions till the 
edges of the paper. If the paper is very big, the line 
can be very long, too. 
How long would the line be on a playing field?
Let’s discuss. 
  Complete the rangoli. Then, have a class  
discussion with the help of the following questions :
(1) What kind of surface do you need for making
a rangoli?
(2) How do you start making a rangoli?
(3) What did you do in order to complete the
rangoli?
(4) Name the different shapes you see in the
rangoli.
(5)	 Would it be possible to make a rangoli on a
scooter or on an elephant’s back?
(6)	 When making a rangoli on paper, what do you
use to make the dots?
Let’s learn.
A
P
T
?? ?? ?? 2
 Look at the pictures. What do you see? 
Rays starting from the sun go forward in all 
directions. Light rays from the torch also 
start from a point and go forward 
continuously in one direction. 
P
Q
 A ray is a part of a line. It starts at one point and goes 
forward continuously in the same direction. The starting point 
of a ray is called its origin. Here, P is the origin. An arrowhead is drawn to show that the 
ray is infinite in the direction of Q. The figure can be read as ray PQ. 
The ray PQ is not read as ray QP.
 Let’s imagine that we can extend this line forever 
without any limits on both sides. To show this extended 
line on paper, we use arrowheads at both ends of the 
line. In mathematics, when we say line, we mean ‘straight 
line’. The first line that we drew was only from point A 
to point B. It was a piece or a segment of the longer line. 
A line segment has two points showing its limits. They 
are  called  endpoints.  We  write  line  segment  AB  as 
‘seg AB’ in short. A and B are its endpoints. A line is 
named using a small letter or by using any two points on 
the line. Line l has been shown alongside. Its name can 
also be written as line PQ or line QP. 
Rays
A
B
P Q
Activity 1 : Draw a point on the blackboard. Every student now 
draws a line that passes through that point. 
How many such lines can be drawn? 
Activity 2 : Draw a point on a paper and use your ruler to draw lines 
that pass through it. How many such lines can you draw?
An infinite number of lines can be drawn through one point. 
 When two or more lines pass through the same point, they are called concurrent 
lines and the common point through which they pass is called their point of concurrence. 
In the figure alongside, which is the point of concurrence? Name it.
Try this.
P
l
3
    
Planes
 Look at the pictures. What 
kind of surfaces do you see? 
   The surfaces in the first 
two pictures are flat. Each flat 
surface is a part of an infinite 
surface. In mathematics, a 
flat surface is called a plane.
 The name of the plane in the picture is ‘H’. Even 
though we draw a suitably small figure of the plane, it 
actually extends infinitely on all sides. Arrows are drawn 
to show that the plane extends infinitely in all directions. 
However, these arrows are often omitted for the sake of 
convenience.
There are 9 points in this figure. Name them. 
If you choose any two points, how many lines can 
pass through the pair? 
One and only one line can be drawn through any 
two distinct points. 
Which three or more of these nine points lie on a 
straight line? Three or more points which lie on a 
single straight line are said to be collinear points. Of these nine points, name any three 
or more points which do not lie on the same line. Points which do not lie on the same 
line are called non- collinear points. 
Can you tell?
H
Parallel Lines 
 Look at this page from a notebook. Is this page a part of a plane? 
If we extend the lines that run sideways on the page, will they meet 
each other somewhere?
Lines which lie in the same plane but do not intersect are said to be 
parallel to each other.
Let’s learn.
Now I know -
Page 4


1
B
1
PART ONE
Basic Concepts in Geometry 
A
B
A
        Points
 A point is shown by a tiny dot. We can use a 
pen or a sharp pencil to make the dot. The dots in 
the rangoli are the symbols for points. 
 A point can be given a name. Capital letters of 
the alphabet are used to name a point. The points 
P, A and T are shown in the figure alongside.
Line Segments and Lines
 Take two points A and B on a sheet of paper 
and join them using a ruler. We get the straight line 
AB. Can we extend this line further on the side of          
point B? On the side of point A? How far can we 
extend it?
 We can extend the line in both directions till the 
edges of the paper. If the paper is very big, the line 
can be very long, too. 
How long would the line be on a playing field?
Let’s discuss. 
  Complete the rangoli. Then, have a class  
discussion with the help of the following questions :
(1) What kind of surface do you need for making
a rangoli?
(2) How do you start making a rangoli?
(3) What did you do in order to complete the
rangoli?
(4) Name the different shapes you see in the
rangoli.
(5)	 Would it be possible to make a rangoli on a
scooter or on an elephant’s back?
(6)	 When making a rangoli on paper, what do you
use to make the dots?
Let’s learn.
A
P
T
?? ?? ?? 2
 Look at the pictures. What do you see? 
Rays starting from the sun go forward in all 
directions. Light rays from the torch also 
start from a point and go forward 
continuously in one direction. 
P
Q
 A ray is a part of a line. It starts at one point and goes 
forward continuously in the same direction. The starting point 
of a ray is called its origin. Here, P is the origin. An arrowhead is drawn to show that the 
ray is infinite in the direction of Q. The figure can be read as ray PQ. 
The ray PQ is not read as ray QP.
 Let’s imagine that we can extend this line forever 
without any limits on both sides. To show this extended 
line on paper, we use arrowheads at both ends of the 
line. In mathematics, when we say line, we mean ‘straight 
line’. The first line that we drew was only from point A 
to point B. It was a piece or a segment of the longer line. 
A line segment has two points showing its limits. They 
are  called  endpoints.  We  write  line  segment  AB  as 
‘seg AB’ in short. A and B are its endpoints. A line is 
named using a small letter or by using any two points on 
the line. Line l has been shown alongside. Its name can 
also be written as line PQ or line QP. 
Rays
A
B
P Q
Activity 1 : Draw a point on the blackboard. Every student now 
draws a line that passes through that point. 
How many such lines can be drawn? 
Activity 2 : Draw a point on a paper and use your ruler to draw lines 
that pass through it. How many such lines can you draw?
An infinite number of lines can be drawn through one point. 
 When two or more lines pass through the same point, they are called concurrent 
lines and the common point through which they pass is called their point of concurrence. 
In the figure alongside, which is the point of concurrence? Name it.
Try this.
P
l
3
    
Planes
 Look at the pictures. What 
kind of surfaces do you see? 
   The surfaces in the first 
two pictures are flat. Each flat 
surface is a part of an infinite 
surface. In mathematics, a 
flat surface is called a plane.
 The name of the plane in the picture is ‘H’. Even 
though we draw a suitably small figure of the plane, it 
actually extends infinitely on all sides. Arrows are drawn 
to show that the plane extends infinitely in all directions. 
However, these arrows are often omitted for the sake of 
convenience.
There are 9 points in this figure. Name them. 
If you choose any two points, how many lines can 
pass through the pair? 
One and only one line can be drawn through any 
two distinct points. 
Which three or more of these nine points lie on a 
straight line? Three or more points which lie on a 
single straight line are said to be collinear points. Of these nine points, name any three 
or more points which do not lie on the same line. Points which do not lie on the same 
line are called non- collinear points. 
Can you tell?
H
Parallel Lines 
 Look at this page from a notebook. Is this page a part of a plane? 
If we extend the lines that run sideways on the page, will they meet 
each other somewhere?
Lines which lie in the same plane but do not intersect are said to be 
parallel to each other.
Let’s learn.
Now I know -
4
Write the proper term, ‘intersecting lines’ or ‘parallel lines’ in each of the empty boxes.
 Observe the picture of the 
game being played. Identify the 
collinear players, non- collinear 
players,  parallel  lines  and          
the plane.
 In January, we can see the constellation 
of Orion in the eastern sky after seven in the 
evening. Then it moves up slowly in the sky. 
Can you see the three collinear stars in this 
constellation? Do you also see a bright star 
on the same line some distance away?
1. Look at the figure alongside and
name the following :
(1) Collinear points
(2) Rays
(3) Line segments
(4) Lines
2. Write the different names of the line.
M
P
T
R
S
O
N
A D C B
l
Practice Set 1
 My friend, Maths : On the ground, in the sky.
Page 5


1
B
1
PART ONE
Basic Concepts in Geometry 
A
B
A
        Points
 A point is shown by a tiny dot. We can use a 
pen or a sharp pencil to make the dot. The dots in 
the rangoli are the symbols for points. 
 A point can be given a name. Capital letters of 
the alphabet are used to name a point. The points 
P, A and T are shown in the figure alongside.
Line Segments and Lines
 Take two points A and B on a sheet of paper 
and join them using a ruler. We get the straight line 
AB. Can we extend this line further on the side of          
point B? On the side of point A? How far can we 
extend it?
 We can extend the line in both directions till the 
edges of the paper. If the paper is very big, the line 
can be very long, too. 
How long would the line be on a playing field?
Let’s discuss. 
  Complete the rangoli. Then, have a class  
discussion with the help of the following questions :
(1) What kind of surface do you need for making
a rangoli?
(2) How do you start making a rangoli?
(3) What did you do in order to complete the
rangoli?
(4) Name the different shapes you see in the
rangoli.
(5)	 Would it be possible to make a rangoli on a
scooter or on an elephant’s back?
(6)	 When making a rangoli on paper, what do you
use to make the dots?
Let’s learn.
A
P
T
?? ?? ?? 2
 Look at the pictures. What do you see? 
Rays starting from the sun go forward in all 
directions. Light rays from the torch also 
start from a point and go forward 
continuously in one direction. 
P
Q
 A ray is a part of a line. It starts at one point and goes 
forward continuously in the same direction. The starting point 
of a ray is called its origin. Here, P is the origin. An arrowhead is drawn to show that the 
ray is infinite in the direction of Q. The figure can be read as ray PQ. 
The ray PQ is not read as ray QP.
 Let’s imagine that we can extend this line forever 
without any limits on both sides. To show this extended 
line on paper, we use arrowheads at both ends of the 
line. In mathematics, when we say line, we mean ‘straight 
line’. The first line that we drew was only from point A 
to point B. It was a piece or a segment of the longer line. 
A line segment has two points showing its limits. They 
are  called  endpoints.  We  write  line  segment  AB  as 
‘seg AB’ in short. A and B are its endpoints. A line is 
named using a small letter or by using any two points on 
the line. Line l has been shown alongside. Its name can 
also be written as line PQ or line QP. 
Rays
A
B
P Q
Activity 1 : Draw a point on the blackboard. Every student now 
draws a line that passes through that point. 
How many such lines can be drawn? 
Activity 2 : Draw a point on a paper and use your ruler to draw lines 
that pass through it. How many such lines can you draw?
An infinite number of lines can be drawn through one point. 
 When two or more lines pass through the same point, they are called concurrent 
lines and the common point through which they pass is called their point of concurrence. 
In the figure alongside, which is the point of concurrence? Name it.
Try this.
P
l
3
    
Planes
 Look at the pictures. What 
kind of surfaces do you see? 
   The surfaces in the first 
two pictures are flat. Each flat 
surface is a part of an infinite 
surface. In mathematics, a 
flat surface is called a plane.
 The name of the plane in the picture is ‘H’. Even 
though we draw a suitably small figure of the plane, it 
actually extends infinitely on all sides. Arrows are drawn 
to show that the plane extends infinitely in all directions. 
However, these arrows are often omitted for the sake of 
convenience.
There are 9 points in this figure. Name them. 
If you choose any two points, how many lines can 
pass through the pair? 
One and only one line can be drawn through any 
two distinct points. 
Which three or more of these nine points lie on a 
straight line? Three or more points which lie on a 
single straight line are said to be collinear points. Of these nine points, name any three 
or more points which do not lie on the same line. Points which do not lie on the same 
line are called non- collinear points. 
Can you tell?
H
Parallel Lines 
 Look at this page from a notebook. Is this page a part of a plane? 
If we extend the lines that run sideways on the page, will they meet 
each other somewhere?
Lines which lie in the same plane but do not intersect are said to be 
parallel to each other.
Let’s learn.
Now I know -
4
Write the proper term, ‘intersecting lines’ or ‘parallel lines’ in each of the empty boxes.
 Observe the picture of the 
game being played. Identify the 
collinear players, non- collinear 
players,  parallel  lines  and          
the plane.
 In January, we can see the constellation 
of Orion in the eastern sky after seven in the 
evening. Then it moves up slowly in the sky. 
Can you see the three collinear stars in this 
constellation? Do you also see a bright star 
on the same line some distance away?
1. Look at the figure alongside and
name the following :
(1) Collinear points
(2) Rays
(3) Line segments
(4) Lines
2. Write the different names of the line.
M
P
T
R
S
O
N
A D C B
l
Practice Set 1
 My friend, Maths : On the ground, in the sky.
5
 
Maths is fun !
Take a flat piece of thermocol or cardboard, a 
needle and thread. Tie a big knot or button or 
bead at one end of the thread. Thread the needle 
with the other end. Pass the needle up through 
any convenient point P. Pull the thread up, leaving 
the knot or the button below. Remove the needle 
and put it aside. Now hold the free end of the 
thread and gently pull it straight. Which figure do 
you see? Now, holding the thread straight, turn it 
in different directions. See how a countless number of lines can pass through a single 
point P.
3. Match the following :
 Group A Group B
(a) Ray
  
(b) Plane
(c) Line
(d) Line segment
4. Observe the figure below. Name the parallel lines, the concurrent lines and the points
of concurrence in the figure.
Use the tools of the Geogebra software to draw various points, lines and rays. 
See for yourself what a never ending line is like.
(i)
(ii)
(iii)
(iv)
a
b
c
A
m
C
D
p
q
?????? ICT Tools or Links
P