NCERT Solutions for Class 6 Maths Chapter 2 – Lines and Angles (रेखाएँ और कोण)
This chapter is a part of the Mathematics textbook for Class 6 under the CBSE syllabus prescribed by the National Council of Educational Research and Training. It introduces basic geometry—how to identify, draw, and measure lines, rays, and angles. Each exercise in this chapter strengthens logical understanding through visual and practical examples.
Table of Contents
- Introduction
- Key Concepts of Lines and Angles
- Exercise-wise Solutions
- Download NCERT Class 6 Maths Chapter 2 PDF
- Frequently Asked Questions
Introduction
Geometry forms the foundation of Mathematics and is used in our surroundings—from the shape of windows to road intersections. In this chapter, students learn to differentiate between line segments, rays, and angles. Each concept is supported by clear illustrations and examples to help students visualize geometric figures accurately.
Key Concepts Explained
1. Point and Line
A point shows an exact position or location. A line extends endlessly in both directions. The NCERT textbook explains that through one point, infinite lines can pass, but through two points, only one unique line can pass.
\(\text{If A and B are two points, then line } \overleftrightarrow{AB} \text{ passes through them.}\)
2. Line Segment
A line segment has two endpoints. It is represented as \( \overline{AB} \). Unlike a line, it does not extend infinitely.
3. Ray
A ray starts from a fixed point and extends infinitely in one direction. It is denoted as \( \overrightarrow{AB} \).
4. Angle
An angle is formed when two rays meet at a common point (the vertex). The size of an angle is measured in degrees.
\(\angle AOB = 40^{\circ}\)
5. Types of Angles
Depending on the measure, angles are classified as follows:
| Type of Angle | Measure | Example |
|---|---|---|
| Acute Angle | Less than 90° | 45° |
| Right Angle | Exactly 90° | 90° |
| Obtuse Angle | Between 90° and 180° | 120° |
| Straight Angle | Exactly 180° | 180° |
| Reflex Angle | Between 180° and 360° | 270° |
Exercise-wise Solutions
Below is a summary of the important exercises covered in the NCERT Class 6 Maths Chapter 2 Lines and Angles.
Exercise 2.1
Topic: Identification of lines, rays, and line segments
Students are taught to differentiate between lines, rays, and line segments using figures. Example: Rehan and Sheetal’s activity shows that infinite lines can pass through a point, but only one line can pass through two distinct points.
Exercise 2.2
Topic: Naming of line segments and intersection of lines
Students learn to name line segments and recognize points that lie on single or multiple segments. For example, in figure \( \overline{LM}, \overline{\MP}, \overline{PQ} \), and \( \overline{QR} \), point M lies on two line segments.
Exercise 2.3
Topic: Understanding Rays and Angles
By identifying rays such as \( \overrightarrow{TA}, \overrightarrow{TB}, \overrightarrow{TN} \), students learn that the starting point of all rays is common (vertex T).
Exercise 2.4
Topic: Measuring Angles using a Protractor
Students learn to measure various types of angles using a protractor. They also study that the sum of angles in a triangle is always 180°.
\(\angle A + \angle B + \angle C = 180^{\circ}\)
Exercise 2.5
Topic: Practical Geometry Activities
Using folding paper or a protractor, students perform activities to identify and measure right angles, acute angles, and obtuse angles. It encourages visualization and hands-on geometry.
Download NCERT Class 6 Maths Chapter 2 Lines and Angles PDF
Students can download the official NCERT PDF for Class 6 Maths Chapter 2 – Lines and Angles from the official NCERT and NCERTBooks.net portals. These are essential for offline study and CBSE exam preparation.
| Book Title | Download Link (Official NCERT PDF) |
|---|---|
| Class 6 Mathematics – Chapter 2 Lines and Angles | Download PDF |