Lines and Angles – Complete Guide For Class 7 Math Chapter 5

Welcome to iPrep, your Learning Super App. Our learning resources for the chapter, Lines and Angles in Mathematics for Class 7th are designed to ensure that you grasp this concept with clarity and perfection. Whether you’re studying for an upcoming exam or strengthening your concepts, our engaging animated videos, practice questions and notes offer you the best of integrated learning with interesting explanations and examples. 

The chapter on Lines and Angles introduces the fundamental concepts of geometry, essential for understanding the relationships between different geometric shapes and their properties. Students learn to identify and classify various types of angles, such as acute, right, obtuse, straight, and reflex angles, and understand how they are measured. This chapter emphasizes the importance of recognizing angle pairs, including complementary, supplementary, adjacent, and vertically opposite angles, and how these pairs interact when intersected by a transversal. Mastery of these concepts is critical for tackling more advanced geometric problems in higher-level mathematics and applying these skills to real-life situations, such as in architecture, engineering, and design.

Lines and Angles

There are various basic definitions covered in the chapter lines and angles, which include:

Point

A point is a precise location or position in a geometric space. It is an exact position but has no length, width, or thickness. Points are usually denoted by capital letters such as A, B, or C.

• Example: Point A is a specific location on a plane.

Line

A line is a straight one-dimensional figure that extends infinitely in both directions. It has no endpoints and is often represented by a line with two arrowheads indicating that it continues indefinitely.

• Example: Line AB extends infinitely in both directions through points A and B.

Line Segment

A line segment is a part of a line that is bounded by two distinct endpoints. It has a definite beginning and end, and it includes all the points between these endpoints.

• Example: Line segment CD is the part of the line that starts at point C and ends at point D.

Angles

An angle is formed when two line segments or two rays have a common end-point.

Examples of Angles:

Types of Angles

Within the chapter lines and angles, there is mention of various types of angles which include:

• Acute Angle: An acute angle is less than 90°.

• Right Angle: A right angle is exactly 90°.

• Obtuse Angle: An obtuse angle is greater than 90° but less than 180°.

• Straight Angle: A straight angle is exactly 180°.

• Reflex Angle: A reflex angle is between 180° and 360°.

Measurement of an Angle

Within the chapter lines and angles, we also get to learn the concept of measurement of an angle. So here is how yo measure and angle:

Related Angles

Within the chapter lines and angles, we also get an understanding of Related angles. Some types of related angles include:

Complementary Angles

When the sum of measures of two angles is 90°, they are called complementary angles.

Example of Complementary Angles: In all sets, the sum of angles is 90°, making them complementary.

Supplementary Angles

When the sum of measures of two angles is 180°, they are called supplementary angles.

Example of Supplementary Angles: In all sets, the sum of angles is 180°, making them supplementary.

Adjacent Angles

At vertex O, a pair of angles are placed next to each other.

Characteristics:

• They have a common vertex.
• They have a common arm.
• The non-common arms are on either side of the common arm.

Example of Adjacent Angles: In all angles, one common vertex has several angles placed next to each other. So all these angles are adjacent angles

Linear Pair

A linear pair is a pair of adjacent angles whose non-common sides are opposite rays.

Example of Linear Pair:

Vertically Opposite Angles

When two angles are formed by two intersecting lines, lying on opposite sides of the point of intersection, it is called vertically opposite angles.

Example of Vertically Opposite Angles: A pair of vertically opposite angles are: 

• Angle AOX and Angle YOB. 
• Angle AOY and angle XOB. 

Pair of Lines

The chapter 5- “lines and angles” also covers the concept of Pair of Lines. Some examples of pairs of lines include:

Intersecting Lines

Intersecting lines are two or more lines that meet or cross each other at a single point. This point of intersection is where the lines share exactly one common point.

Examples:

• The letter “X” is formed by two intersecting lines. These lines meet at a single point in the middle of the letter.       
• The blades of a pair of scissors are two lines that intersect at the pivot point. As the blades open and close, they continue to intersect at this single point.

Transversal

A line that intersects two or more lines at distinct points is called a transversal.

Example of Transversal: Line ‘o’ intersecting lines L, M, N at distinct points 1, 2, 3. Thus, line “o” is a transversal.

Angles Made by a Transversal: When lines l and m are cut by transversal p, eight angles are formed, each with a special name.

Table of Angles

Transversals of parallel lines give rise to quite interesting results. 

Corresponding Angles: If two parallel lines are cut by a transversal, each pair of corresponding angles is equal.

Alternate Interior Angles: If two parallel lines are cut by a transversal, each pair of alternate interior angles is equal.

Pair of Supplementary Angles: If two parallel lines are cut by a transversal, each pair of interior angles on the same side of the transversal are supplementary.

Checking for Parallel Lines:

To determine if two lines are parallel: If a transversal gives rise to pairs of equal corresponding angles, equal alternate interior angles, and supplementary interior angles on the same side, then the lines are parallel.

         Examples: 

• When a transversal “L” cuts two lines A and B, and angle 1 equals angle 2, lines A and B are parallel.

• When a transversal cuts two lines such that pairs of alternate interior angles are equal, the lines are parallel.

• When a transversal cuts two lines such that pairs of interior angles on the same side of the transversal are supplementary, the lines are parallel.

In conclusion, the chapter on Lines and Angles provides a crucial foundation in geometry and iPrep’s resources on CLass 7th math Chapter 5 – Lines and Angles are designed to make mastering these concepts both engaging and effective. From understanding different types of angles to exploring their relationships and properties, our animated videos, practice questions, and notes offer a comprehensive approach to learning. By leveraging these tools, you’ll not only prepare for exams with confidence but also gain valuable skills applicable to various real-world scenarios. Dive into the chapter Lines and Angles with iPrep and strengthen your grasp of geometry for future academic success.