Lines and Angles – Class 6 Maths Chapter 2 Notes & NCERT PDF

Introduction

This chapter builds the "building blocks" of plane geometry: points, line segments, lines, rays and angles. It then shows how to compare, measure, draw and classify angles — and why a full turn has 360 degrees.

Key Ideas

2.1 Point

A point marks a precise location. It has no length, breadth or height. Models: the tip of a compass, the sharpened end of a pencil, the pointed end of a needle. Points are named with capital letters: Point Z, Point P, Point T.

2.2 Line Segment

The shortest path from point A to point B (including A and B) is called the line segment AB (or BA).

A crease in folded paper is a model. A and B are its end points.

2.3 Line

Extend segment AB forever beyond both ends and you get a line AB (sometimes named l or m). You can never draw a complete line. Any two points determine exactly one line — but through one point you can draw countless lines (Rihan and Sheetal's question).

2.4 Ray

A ray starts at one point and goes on endlessly in one direction — like a beam from a lighthouse, a torch, or sun rays. Ray OA starts at O and passes through A. If B is also on it, ray OA can be called ray OB, but not ray AO (that would start at A).

2.5 Angle

An angle is formed by two rays having a common starting point.

The common point is the vertex; the rays are the arms. The angle formed by rays BD and BE is written ∠DBE or ∠EBD — the vertex is always the middle letter. The size of an angle is the amount of rotation (turn) needed about the vertex to move one arm onto the other — as when Vidya opens her book cover wider and wider.

2.6 Comparing Angles

2.7 Making Rotating Arms

Two paper straws joined by a paper clip make "rotating arms". In the slit activity only the arms whose angle equals the slit's angle pass through — arm length does not matter.

2.8 Special Types of Angles

2.9 Measuring Angles

The angle at the centre of a circle is divided into 360 equal parts; each is 1 degree (1°).

2.10 Drawing Angles

To draw ∠TIN = 30°: draw arm IN, put the protractor's centre on I with IN along the 0 line, count up to 30 and mark T, then join I to T.

2.11 Types of Angles and their Measures

Worked Examples

Figure it Out — Hints

Maths Words

Common Mistakes

Maths in Daily Life

Angles appear in clock hands, opening doors, scissors, compasses, spectacles, swings (a bigger starting angle gives more speed), slopes of slides and roads, and giving directions.