Chapter 2 — Lines and Angles

Chapter 2 of the Class 6 Maths NCERT textbook (Ganita Prakash), "Lines and Angles", introduces the fundamental building blocks of geometry — points, line segments, lines, rays and angles — and teaches students how to classify, compare and measure angles using a protractor.

• The basic geometric objects — Geometry starts from a point, which only marks a location. A line segment is the shortest path between two points, a line extends it infinitely both ways, and a ray extends infinitely in one direction from a start point.
• What an angle really measures — An angle is formed by two rays (arms) sharing a common vertex, and its size is the amount of turn needed to move one arm onto the other. Crucially, arm length does not change the angle's size.
• Classifying and measuring angles — Angles are named acute, right, obtuse, straight or reflex by size, with a full turn being 360°. A protractor divides a semicircle into 180 equal parts so angles can be measured and drawn precisely in degrees.

1. 01A point has no length, breadth or height — it only marks a precise location, denoted by a capital letter.
2. 02A line segment is the shortest path between two points; a line is a line segment extended infinitely in both directions; a ray starts at one point and extends infinitely in one direction.
3. 03Exactly one unique line passes through any two distinct points; infinitely many lines pass through a single point.
4. 04An angle is formed by two rays with a common starting point called the vertex; the two rays are called the arms.
5. 05The size of an angle equals the amount of rotation (turn) about the vertex — arm length does not affect angle size.
6. 06Angles are classified as: acute (0°–90°), right (exactly 90°), obtuse (90°–180°), straight (180°) and reflex (180°–360°).
7. 07One full turn = 360°; a straight angle = 180°; a right angle = 90°; a right angle is 1/4 of a full turn.
8. 08Two lines meeting at right angles are called perpendicular lines; a right angle resembles the letter L.
9. 09A protractor (semi-circle divided into 180 equal parts) is used to measure and draw angles in degrees.
10. 10The angle bisector divides an angle into two equal halves; repeated paper folding bisects angles (e.g., 180° → 90° → 45° → 22.5°).
11. 11The Ashoka Chakra has 24 spokes, so adjacent spokes are 360° ÷ 24 = 15° apart; the largest acute angle between spokes is 75°.
12. 12The choice of 360° for a full turn comes partly from ancient texts (Rigveda: wheel with 360 spokes) and the fact that 360 divides evenly by all integers from 1 to 10 except 7.