NCERT Class 6 Maths Chapter 2 Lines and Angles – Complete Notes and Solutions | Ganita Prakash
NCERT Class 6 Maths Chapter 2 – Lines and Angles
Complete Explanation and Solved Questions
Introduction
Geometry helps us understand shapes, space, and position. One of the most important ideas in geometry is the concept of lines and angles.
Whenever two lines meet at a point, they form an angle. We see angles everywhere around us:
scissors
clock hands
open doors
bicycle wheels
In this chapter from Ganita Prakash (NCERT Class 6), students learn:
basic geometric terms
types of lines
angles and their parts
how to name and compare angles
Understanding these concepts will help you in higher classes as well.
Basic Terms and Definitions
1. Point
A point represents an exact location.
It has no size, length, or width.
Points are named using capital letters.
Example:
Point A, Point B, Point C
2. Line
A line is a straight path that extends infinitely in both directions.
It has no endpoints.
Example:
Line AB
3. Line Segment
A line segment is part of a line with two endpoints.
Example:
Segment AB
4. Ray
A ray starts from one point and extends infinitely in one direction.
Example:
Ray AB
A is the starting point.
Understanding Angles
An angle is formed when two rays meet at a common point.
Parts of an Angle
Vertex → common point
Arms → the two rays forming the angle
Example:
Angle ABC
Here
B = vertex
BA and BC = arms
Real Life Examples of Angles
Angles appear in many everyday objects:
scissors
ladder against wall
open book
bicycle frame
These objects show how one arm rotates around another arm.
Figure Based Questions
This figure contains angles formed by different rays with common points.
Question 1
Draw and label an angle with arms ST and SR.
Solution
Step 1
Mark a point S on paper.
Step 2
Draw one ray from S towards T.
Step 3
Draw another ray from S towards R.
Step 4
The angle formed is written as
∠TSR or ∠RST
S is the vertex.
Question 2
Explain why ∠APC cannot be labeled as ∠P.
Solution
Sometimes more than one angle is formed at the same vertex.
At point P, there may be multiple rays:
PA
PB
PC
So there could be angles:
∠APB
∠BPC
∠APC
If we write only ∠P, it becomes unclear which angle we mean.
Therefore, we use three letters to name the angle.
This diagram helps students see how different angles share the same vertex.
Question 3
Name the angles marked in the figure.
Step-by-Step Solution
Step 1
Identify the vertex.
Step 2
Look at the two rays forming each angle.
Step 3
Name angles using three letters where the vertex stays in the middle.
Example
If rays are
QP and QR
Then angle name is
∠PQR
Comparing Angles
Angles can be compared in two ways:
By observation
By superimposition
Method 1: Observation
The angle that opens wider is the larger angle.
Example
If
∠A > ∠B
Then A is larger.
Method 2: Superimposition
In this method:
Draw two angles.
Place one angle on top of the other.
Align the vertices and one arm.
If the other arm overlaps exactly, the angles are equal.
This figure from the book shows how angles are compared by overlapping them.
Practice Question
Draw four rays starting from point O.
Label them
OA
OB
OC
OD
How many angles are formed?
Possible angles:
∠AOB
∠BOC
∠COD
∠AOC
∠BOD
∠AOD
Total = 6 angles
Important Tips for Students
✔ Always keep the vertex in the middle while naming angles
✔ Use capital letters for points
✔ Draw diagrams neatly
✔ Practice identifying angles in daily objects
Quick Revision
A point shows position.
A line extends infinitely.
A ray has one endpoint.
An angle is formed when two rays meet.
Angles are named using three letters, with the vertex in the midConclusion
The chapter Lines and Angles builds the foundation of geometry. Once students clearly understand points, rays, and angles, they will find later topics like triangles and polygons much easier.
Regular practice of diagrams and naming angles will strengthen your concepts.
For more clear explanations and solved questions, keep visiting
Fuzymath Academy
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