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

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