Class 6 ยท Maths ยท Ganita Prakash
Chapter 2 ๐
Chapter 2 ๐
Lines and Angles
Quick, colourful revision notes โ easy to read before your test!
Chapter Contents
2.1 โ 2.4 Point, Line Segment, Line & Ray
These are the basic building blocks of geometry โ the shapes we study are all made of these!
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Fig 1: Point, Line Segment, Line and Ray compared
Point โ an exact location, shown with a dot and named with a capital letter (e.g. Point A).
Line segment AB โ the shortest path joining two points A and B. Has 2 fixed end points.
Line AB โ a line segment extended endlessly on both sides. Written AB with arrows, or a small letter like l or m.
Ray AP โ starts at point A and goes on endlessly in one direction only.
Line segment AB โ the shortest path joining two points A and B. Has 2 fixed end points.
Line AB โ a line segment extended endlessly on both sides. Written AB with arrows, or a small letter like l or m.
Ray AP โ starts at point A and goes on endlessly in one direction only.
Any two points determine exactly one unique line passing through both of them.
2.5 What is an Angle?
An angle is formed by two rays that share a common starting point.
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Fig 2: Parts of an angle
Vertex โ the common starting point (B).
Arms โ the two rays that form the angle (BD and BE).
We name it โ DBE or โ EBD โ the vertex letter is always written in the middle.
Arms โ the two rays that form the angle (BD and BE).
We name it โ DBE or โ EBD โ the vertex letter is always written in the middle.
The size of an angle is the amount of rotation (turn) needed to bring one arm onto the other โ not the length of the arms! A short-armed angle and a long-armed angle can have the exact same size.
Real-life angles: opening a book cover, a pair of scissors, a compass/divider, a door opening โ all are formed by rotation about a fixed vertex.
2.6 Comparing Angles
How do we tell which of two angles is bigger?
Superimposition โ placing one angle exactly over another (matching the vertices) to see which is larger. If the arms of both angles also match exactly, the angles are equal.
Without tracing paper, a see-through circle can help: place its centre on the vertex, mark where the arms cross the circle's edge, then compare on the other angle the same way.
A bigger arm length does NOT mean a bigger angle! Only the amount of turn between the arms matters.
2.8 Special Angles
Straight angle โ arms lie exactly opposite, in one straight line (a half turn).
Right angle โ exactly half of a straight angle (looks like the letter 'L').
Perpendicular lines โ two lines that meet each other at a right angle.
Angle bisector โ a ray/line that cuts an angle into two exactly equal halves.
Right angle โ exactly half of a straight angle (looks like the letter 'L').
Perpendicular lines โ two lines that meet each other at a right angle.
Angle bisector โ a ray/line that cuts an angle into two exactly equal halves.
A straight angle = 2 right angles placed together.
2.9 โ 2.10 Measuring Angles
A full turn (full circle) is divided into 360 equal parts. Each part is 1 degree (1ยฐ) โ the standard unit for measuring angles.
| Turn | Degree Measure |
|---|---|
| Full turn (complete circle) | 360ยฐ |
| Half turn (straight angle) | 180ยฐ |
| Quarter turn (right angle) | 90ยฐ |
A protractor is a tool used to measure angles in degrees โ usually a half-circle marked from 0ยฐ to 180ยฐ.
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Fig 3: Measuring โ TIN = 30ยฐ using a protractor โ place the vertex I at the centre, align arm IN to 0ยฐ, then read where arm IT crosses the scale
Steps to measure an angle: (1) Place the protractor's centre exactly on the vertex. (2) Align one arm with the 0ยฐ line. (3) Read the degree mark where the second arm crosses the scale.
Why 360ยฐ? It's an old convention (linked to ancient calendars of ~360 days) that stuck because 360 divides evenly by almost every number from 1 to 10 (except 7) โ very convenient for splitting circles into equal parts!
2.11 Types of Angles by Measure
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Fig 4: The five types of angles, by degree measure
| Angle Type | Degree Range |
|---|---|
| Acute angle | more than 0ยฐ, less than 90ยฐ |
| Right angle | exactly 90ยฐ |
| Obtuse angle | more than 90ยฐ, less than 180ยฐ |
| Straight angle | exactly 180ยฐ |
| Reflex angle | more than 180ยฐ, less than 360ยฐ |
Acute means "sharp" and obtuse means "blunt" โ that's exactly how these angles look!
๐ฏ Quick Summary
- Point = a location ยท Line segment = 2 end points ยท Line = endless both ways ยท Ray = endless one way.
- An angle = two rays (arms) sharing a common vertex. Size = amount of rotation, not arm length.
- Compare angles by superimposition (matching vertices and arms).
- Straight angle = 180ยฐ = 2 right angles. Right angle = 90ยฐ (โฅ lines meet at right angles).
- Angles are measured in degrees using a protractor. Full turn = 360ยฐ.
- 5 types by measure: Acute (<90ยฐ), Right (90ยฐ), Obtuse (90ยฐโ180ยฐ), Straight (180ยฐ), Reflex (180ยฐโ360ยฐ).
โ๏ธ Notes by @edugrown โ happy revising! ๐