Lines and Angles Class 7 Notes CBSE Maths Chapter 5 (Free PDF Download)

Definitions:

a. Line segment: A line with definite end points is called a line segment. It is denoted as $\overline{AB}$.

b. Line: A line segment when extended infinitely from both ends, we get a line. It is denoted as $\overleftrightarrow{AB}$.

c. Ray: A line with one endpoint is called a ray. It is denoted by $\overrightarrow{AB}$.

d. Angle: When two lines or line segments intersect or meet at a common point, an angle is formed. For example, in the figure below, we can see the angles formed by the lines $\overleftrightarrow{PQ}$ and $\overleftrightarrow{RS}$ are $\angle POS,\angle SOQ,\angle QOR$ and $\angle ROP$.

Related Angles:

a. Complementary angles: Two angles having the sum of their measures equal to ${{90}^{\circ }}$ are called complementary angles. When two angles are complementary, one angle is called the complement of another angle. An example has been shown below.

b. Supplementary angles: Two angles having the sum of their measures equal to ${{180}^{\circ }}$ are called supplementary angles. When two angles are complementary, one angle is called the supplement of another angle. An example has been shown below.

c. Adjacent angle: The pair of angles present next to each other such that they have a common vertex, one common arm and the non-common arm lies on either side of the common arm. In the diagram given below, $\angle 1$ and $\angle 2$ are adjacent angles.

d. Linear pair: The adjacent angles who are supplementary to each other are called the linear pairs. The non-common arms of these angles are rays moving in opposite directions. In the diagram given below, $\angle 1$ and $\angle 2$ are linear pair angles.

e. Vertically opposite angles: Two lines that cross each other, four angles are formed as shown in the diagram below.

Here, $\angle 1\And \angle 3$ and $\angle 2\And \angle 4$ are vertically opposite to each other.

Pairs of Lines:

a. Intersecting lines: two lines when crosses each other at only one point, then they are called the intersecting lines and that point is called the point intersection. As in the diagram below, $l$ and $m$are intersecting lines with their point of intersection $A$.

b. Transversal: When two or more distinct lines are intersected by a common line, then that line is called a transversal. As in the figure below, lines $l$ and $m$ are intersected by a common line $p$ which is the transversal. This transversion creates eight angles.

The relation between the eight angles have been tabulated below.

Traversal of Parallel Lines:

When a pair of parallel lines $l$ and $m$ are intersected by a line $t$, then following properties can be observed.

1. Each pair of corresponding angles are equal. e.g., $\angle 7=\angle 8,\angle 1=\angle 2$, etc.

2. Each pair of alternate interior angles are equal. e.g., $\angle 3=\angle 8,\angle 1=\angle 6$, etc.

3. Each pair of interior angles on the same side of the transversal are supplementary to each other. e.g., $\angle 1+\angle 8={{180}^{\circ }}$, etc.

Introduction To Important Terms

• Lines Segment

A line segment is defined as a line drawn having two endpoints and it is denoted by AB¯.

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(Image will be Uploaded Soon) 

• Line                                             

A line does not have any endpoints on either side and it is denoted by AB←→.

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(Image will be Uploaded Soon) 

If a single straight line passes through 3 or more points, the points are called collinear.

P, Q, R are collinear points.

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(Image will be Uploaded Soon)

• Ray

A ray is described as a line which has one endpoint and is endless from another side. 

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(Image will be Uploaded Soon) 

Pictorial Illustrations and Differentiation Between Line, LineSegment, Ray

You now already know that a line segment consists of two endpoints. If we stretch out the two endpoints in either direction endlessly, we will obtain a line. Thus, remember that a line has no endpoints. On the contrary, a ray consists of one endpoint (starting point). When lines or line segments meet, then an angle is formed. Refer to the image below to understand the difference clearly:-

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(Image will be Uploaded Soon)                 

• Intersecting Line

If two distinct lines cross or meet at a point, then they are termed intersecting lines.

• Parallel Lines

Lines that are at the same distance apart from each other and never bisect anywhere in a plane are called the parallel lines.

• Traversal Line

If a line bisects two or more lines at different points it is known as the traversal line

• Angle

Angles formed are made up of two rays which begin from a common point.

About CBSE Solutions for Lines and Angles Class 7 Notes

In Class 7 Revision Notes Maths Ch 5 available at Vedantu, you will study various types of angles and their applications in geometrical mathematics. Read below about the types of angles you will learn in Class 7 Maths Revision Notes Chapter 5:

Types of Angles

• Acute Angle

An angle which is smaller than 90 degrees is called an acute angle.

• Obtuse Angle

An angle that measures more than 90 degrees but is less than 180 degrees is called an obtuse angle.

• Right Angle

An angle formed at exactly 90 degrees is called a right angle.

• Straight Angle

An angle formed at 180 degrees is called a straight angle. An angle so formed is developed by a straight line.

• Reflex Angle

An angle more than 180 degrees but less than 270 degrees is called a reflex angle.

• Full Angle

A full angle is an angle that measures complete 360°.

Other Types of Angles

• Complementary Angles: The sum of the measures of two angles comes out to be 90°, the angles formed are what we call the complementary angles.

e.g. ∠A = 65°, ∠B = 25°

∠A + ∠B = 65° + 25° = 90°

• Supplementary Angles: When the sum of the measures of the two angles is 180° and then such pairs of angles are known as supplementary angles.

e.g. ∠A = 140°, ∠B = 40°

∠A + ∠B = 140° + 40° = 180°

• Adjacent Angles: These angles are that which consists of a common vertex, a common arm and non-common arms on either side of the common arm are called adjacent angles. Adjacent angles have no common interior points.

• Linear Pair: A pair of adjacent angles whose non-common sides make for opposite rays is called a linear pair.

• Vertically Opposite Angles: when two lines bisect each other, the vertically opposite angles so formed are equivalent.

Solved Examples

Example:

Find the angle which will be equal to its complement.

Solution:

Assuming the two equal complementary angles be x

Thus, x + x = 90°

Or, 2x = 90°

And x = 90/2 = 45°

Thus, 45 is equivalent to its complement.

Example:

If in a plane figure AB∥CD with ∠4 = 50° and ∠5 = 45°, then identify all the three angles of the ∆ABC.

Solution:

Given:  AB ∥ CD

∠4 = 60° and ∠5 = 40°

In order to identify: ∠1, ∠2 and ∠3

Calculation: ∠1 + ∠4 + ∠5 = 180° (sum of angles forming a straight angle)

Thus, ∠1 = 180°- 60°- 40°

∠1 = 80°

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• Solving "Lines and Angles Class 7 Notes CBSE Maths Chapter 5 (Free PDF Download)" offers several noteworthy benefits to students. 

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Prepare Well for Lines and Angles Class 7 Notes CBSE Maths Chapter 5 

In conclusion, "Lines and Angles Class 7 Notes CBSE Maths Chapter 5 (Free PDF Download)" serves as an invaluable educational resource. This chapter is fundamental in building students' geometric understanding and problem-solving skills. The notes provide clarity on geometric principles, aiding in a deeper comprehension of lines and angles. They are a valuable tool for exam preparation, offering comprehensive coverage of the chapter's content. Additionally, these notes encourage critical thinking, logical reasoning, and the practical application of geometry in various fields. Their accessibility as free PDF downloads ensures that quality education is accessible to all, making them an essential companion for students on their mathematical journey.

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