Chapter 2: Lines and Angles
Every shape you draw is made from a few simple parts: points, lines, line segments, rays and angles. In this chapter we name these parts, compare and measure angles in degrees, and use a protractor to draw any angle we like.
In this chapter you will
- tell apart points, line segments, lines and rays, and name them
- name angles and find their vertex and arms
- compare angles by how much they turn
- measure and draw angles with a protractor
- sort angles into acute, right, obtuse, straight and reflex
Topics
- Point, Line Segment, Line and Ray NCERT 2.1–2.4
Point: an exact location, named with a capital letter.
- Angle NCERT 2.5
Two rays that start at the same point (the vertex) make an angle. The rays are its arms.
- Comparing Angles and Rotating Arms NCERT 2.6–2.7
Compare angles by putting one on the other with the vertices together (superimposition).
- Special Types of Angles NCERT 2.8
Full turn: all the way round. Straight angle: half a turn, the arms in one straight line.
- Measuring Angles NCERT 2.9
1 full turn = 360°. Straight angle = 180°. Right angle = 90°.
- Drawing Angles NCERT 2.10
Draw the base arm, put the protractor's centre on the vertex with the base on 0, count to the angle and mark a point, then join.
- Types of Angles and their Measures NCERT 2.11
Acute: 0°–90°. Right: 90°. Obtuse: 90°–180°. Straight: 180°. Reflex: 180°–360°.
Key words
- Point
- an exact location, named with a capital letter
- Line segment
- the shortest path between two points; it has two end points
- Line
- goes on forever in both directions
- Ray
- starts at a point and goes on forever in one direction
- Angle
- two rays with a common starting point
- Vertex
- the common starting point of the arms of an angle
- Degree (°)
- one of the 360 equal parts of a full turn
- Protractor
- a tool for measuring and drawing angles
- Perpendicular
- lines that meet at a right angle
- Angle bisector
- the line that cuts an angle into two equal halves
Summary
- A point marks an exact place. We name it with a capital letter.
- A line segment joins two points and stops at both. A line goes on forever both ways. A ray starts at one point and goes on forever one way.
- Two rays from the same point make an angle. The shared point is the vertex and the rays are the arms.
- How big an angle is depends on how far one arm turns to reach the other, not on how long the arms are.
- We measure angles in degrees with a protractor. A full turn is 360°.
- Angle types: acute (less than 90°), right (90°), obtuse (between 90° and 180°), straight (180°) and reflex (more than 180°).