Lines and Angles notes class 6th
Chapter 2: Lines and Angles
Understand the building blocks of geometry through clear definitions, simple diagrams, solved examples, practice questions and an interactive quiz.
1. Learning Goals
By the end of this chapter, you should be able to:
- Identify a point, line segment, line and ray.
- Recognise intersecting, perpendicular and parallel lines.
- Understand an angle and identify its vertex and arms.
- Classify angles as acute, right, obtuse, straight or reflex.
- Measure and draw angles using a protractor.
2. Basic Ideas: Point, Line Segment, Line and Ray
Point
A point shows an exact position. It has no length, breadth or thickness. We usually name a point with a capital letter, such as A.
Line segment
A line segment is a part of a line with two fixed endpoints. Its length can be measured. Segment AB is written as \(\overline{AB}\).
Line
A line is straight and extends endlessly in both directions. It has no endpoints. The line through A and B is written as \(\overleftrightarrow{AB}\).
Ray
A ray has one fixed endpoint and continues endlessly in one direction. Ray AB starts at A and passes through B, written as \(\overrightarrow{AB}\).
| Shape | Endpoints | Can its length be measured? |
|---|---|---|
| Line segment | Two | Yes |
| Line | None | No finite length |
| Ray | One | No finite length |
3. Types of Lines
Intersecting lines
Two lines are intersecting when they cross or meet at a point.
Parallel lines
Parallel lines remain the same distance apart and never meet, even when extended. The symbol for parallel is \(\parallel\).
Perpendicular lines
Two lines are perpendicular when they meet at a right angle, which measures \(90^\circ\). The symbol is \(\perp\).
4. Understanding Angles
An angle is formed when two rays share a common endpoint. The common endpoint is called the vertex, and the rays are called the arms of the angle.
The angle shown can be named \(\angle ABC\) or \(\angle CBA\). The middle letter, B, is the vertex.
Types of angles
| Type | Measure | Example |
|---|---|---|
| Zero angle | \(0^\circ\) | Both arms overlap in the same direction |
| Acute angle | Greater than \(0^\circ\), less than \(90^\circ\) | \(35^\circ\) |
| Right angle | Exactly \(90^\circ\) | Corner of a square |
| Obtuse angle | Greater than \(90^\circ\), less than \(180^\circ\) | \(120^\circ\) |
| Straight angle | Exactly \(180^\circ\) | A straight line |
| Reflex angle | Greater than \(180^\circ\), less than \(360^\circ\) | \(240^\circ\) |
| Complete angle | Exactly \(360^\circ\) | One full turn |
5. Measuring and Drawing Angles
Using a protractor to measure an angle
- Place the centre mark of the protractor exactly on the angle's vertex.
- Align the protractor's baseline with one arm of the angle.
- Read the scale that starts at \(0^\circ\) on the aligned arm.
- Check whether the angle is acute, right or obtuse to avoid choosing the wrong scale.
To draw an angle of \(60^\circ\)
- Draw a ray OA.
- Place the protractor centre at O and align its baseline with OA.
- Mark the \(60^\circ\) point.
- Draw a second ray from O through the mark. The angle is \(60^\circ\).
6. Solved Examples
Example 1
Classify an angle of \(42^\circ\).
Since \(0^\circ < 42^\circ < 90^\circ\), it is an acute angle.
Example 2
Classify an angle of \(135^\circ\).
Since \(90^\circ < 135^\circ < 180^\circ\), it is an obtuse angle.
Example 3
What is the angle between perpendicular lines?
Perpendicular lines meet at exactly \(90^\circ\), so the angle is a right angle.
Example 4
How many endpoints does a ray have?
A ray has one endpoint and extends endlessly in one direction.
Example 5
Is \(180^\circ\) acute, obtuse or straight?
An angle of \(180^\circ\) is a straight angle.
7. Practice Worksheet
Try these questions before opening the answers.
- How many endpoints does a line segment have?
- What do we call lines that never meet and remain equally far apart?
- Classify \(28^\circ\).
- Classify \(90^\circ\).
- Classify \(164^\circ\).
- What is the measure of a straight angle?
- Which tool is used to measure an angle?
- What is the vertex of an angle?
- How many degrees are there in one complete turn?
- True or false: All intersecting lines are perpendicular.
Show worksheet answers
- Two.
- Parallel lines.
- Acute angle.
- Right angle.
- Obtuse angle.
- \(180^\circ\).
- A protractor.
- The common endpoint of the two rays.
- \(360^\circ\).
- False. Intersecting lines need not meet at \(90^\circ\).
8. Interactive Quiz
Choose one answer for each question, then click Check Answers to see your score and explanations.
9. Quick Revision
- Line segment: two endpoints; measurable length.
- Line: no endpoints; extends in both directions.
- Ray: one endpoint; extends in one direction.
- Parallel lines: never meet.
- Perpendicular lines: meet at \(90^\circ\).
- Acute: between \(0^\circ\) and \(90^\circ\).
- Right: \(90^\circ\); obtuse: between \(90^\circ\) and \(180^\circ\).
- Straight: \(180^\circ\); complete: \(360^\circ\).
- Protractor: tool used to measure angles.