# Chapter 5 – Lines and Angles

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

Lines and angles are the most fundamental and pertinent geometrical concepts. Without these basic structures, it is impossible to understand intricate geometrical shapes any further. Let us take a closer look at what lines and angles are.

#### What is a Line?

What comes to your mind when you think of a line? Is just joining two points anyhow a line? The answer is no; a line is a straight but one-dimensional figure which can extend in both the directions. A line is the most commonly used geometrical shape. A line has length but no width or thickness. Lines make shapes.

#### What is a Ray?

A ray is a combination of a line and a line segment. It has one starting point, and it can extend in only one direction. So, it is not completely like a line segment nor completely like a line either.

#### Pair of Lines

Two or more lines form a pair of lines. But, there are some important concepts to learn with a pair of lines.

• Intersecting pair of lines

It is an intersecting
pair of lines if both the lines or any number of lines have a common point. In the figure above, you can see two intersecting pairs of lines are shown; they also have a common point where both of the lines cross(intersect) each other.
• Parallel pair of lines

If you see two or more lines which do not intersect or cut each other like intersecting
pairs of lines and both the lines follow their path not lie in the same plane, then such pairs of lines are called parallel lines. One way of checking for parallel lines is that they do not meet anywhere at any cost, if so, they are not a parallel pair of lines.
• Transversal pair of lines

Transversal pairs of lines
are the ones where one straight line cuts two or more parallel lines at different points. As you can see in the above figure, there are two parallel lines, and one line cuts them at different or distinct points.

#### Types of Angles

Angles are a very important part of geometry. Pairs of angles which are related to each other in some or other way are called related angles and related angles have given some names which you will see below.

1.     Acute angle
An acute angle is an angle below 90o . So, basically, any angle which measures below 90o is an acute angle. The figure below is an example of an acute angle.
2. Right angle
An angle which measures exactly 90o is called a right angle. A right angle can never be just more or less than 90o . You will get a right angle when two lines are perpendicular to each other.

3. Obtuse angle
An angle which measures more than 90o is called an obtuse angle. This is opposite to acute angle.
4. Complementary angles
If you have two different angles and when you add them, and you get 90o, then the two are complementary angles. If you have an angle 53o and another angle 37o, and if you add these angles, it comes to 53o + 37o = 90o. So, these are complementary angles.
5. Supplementary angles
If you have two different angles and when you add them and you get 180o, then the two are supplementary angles. Suppose you have an angle 120o and another angle 60o – now if you add these angles, it’s 120o + 60o = 180o. So, these are supplementary angles.
When two angles have a common side and a common vertex and they also don’t overlap, those angles are called adjacent angles. For an angle to be adjacent, it must have a common vertex and common side as well.
7. Vertically opposite angles
Now you might be thinking that angles opposite in vertical direction are called vertically opposite angles, but that is not the case. Vertically opposite angles are angles with the same vertex, but they are on either side of the vertex. Vertically opposite angles are always equal to each other.
8. Alternate angles
A set of non-adjacent angles which are not on the same side of the transversal are called alternate angles.
9. Interior angles
The angles which lie inside a polygon are called interior angles.

#### Checking for parallel lines

To check for parallel lines, you have to test these parameters:

• Corresponding angles should be equal.
• Alternate angles should be equal.
• Interior angles on the same side of the transversal should be supplementary.

#### Conclusion

Lines and angles are a very important and fundamental part of geometry and we have learnt the most important and most basic things of geometry, so we will use the concepts of lines and angles of geometry furthermore.

#### FAQs

1. What are the properties of lines and angles?
Properties of lines are:

• Set of three or more points lying on the same line are called collinear points.
• Points not lying on the same line are called non-collinear points.

Properties of angles are:

• An angle greater than 180 degrees but not greater than 360 degrees is called a reflex angle.
• Two adjacent angles adding up to 180 degrees form a linear pair of angles.
2. What are the 5 types of angles?
The five types of angles are acute angle, obtuse angle, right angle, straight angle and reflex angle.
3. How many types of lines and angles are there?
There are a total of nine types of lines and angles.
4. How many types of lines are there?There are four types of lines; horizontal, vertical, parallel and perpendicular lines.
5. Which angles are equal in parallel lines?
If parallel lines are intersected with a transversal then corresponding angle, alternate angle and vertically opposite angle are equal.

To explore more about Lines and Angles through simple, interactive, and explanatory visualizations, download MSVgo. It’ll help you visualise this and more such Mathematics concepts with real life examples and interesting animations.

### High School Physics

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### High School Math

• Algebra – Arithmatic Progressions
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### Middle School Science

• Acids, Bases And Salts
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### Middle School Math

• Area and Its Boundary
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• Tenths and Hundredths
• Time