Ch 2 of Ganita Prakash introduces the fundamental concepts of lines and angles that form the building blocks of geometry. Students learn to identify, name, and measure different types of lines and angles, and explore how these concepts appear in everyday life — from the edges of a book to the hands of a clock.
A point marks a precise location and has no size. A line extends infinitely in both directions and is named using two points on it. A ray starts at one point (endpoint) and extends infinitely in one direction. A line segment is the part of a line between two endpoints. These are the basic elements used to construct all geometric shapes.
An angle is formed when two rays share a common endpoint (vertex). Angles are classified by their measure: acute angles are less than 90°, right angles are exactly 90°, obtuse angles are between 90° and 180°, straight angles are exactly 180°, and reflex angles are between 180° and 360°. A complete turn is 360°.
A protractor is a semi-circular tool used to measure angles in degrees. To measure an angle: place the centre of the protractor on the vertex, align one ray with the 0° line, and read the scale where the other ray crosses. The protractor has two scales (inner and outer) to measure angles opening in either direction.
Two lines that cross at a point are called intersecting lines. When intersecting lines form a 90° angle, they are called perpendicular lines. Lines that never meet, no matter how far extended, are called parallel lines. Railway tracks are a real-world example of parallel lines.
Download the official NCERT PDF for Ch 2 "Lines and Angles" from the NCERT website: https://ncert.nic.in/textbook/pdf/fegp102.pdf. You can also download the complete Ganita Prakash textbook: https://ncert.nic.in/textbook/pdf/fegp1ps.zip
A line extends infinitely in both directions and has no endpoints. A ray has one endpoint and extends infinitely in one direction. A line segment has two endpoints and a definite length.
Place the centre of the protractor on the vertex of the angle. Align one arm of the angle with the 0° baseline. Read the degree where the other arm of the angle crosses the protractor scale.
Two angles are complementary if their sum is 90°. Two angles are supplementary if their sum is 180°. For example, 30° and 60° are complementary; 120° and 60° are supplementary.
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