NCERT Class 9 Maths Chapter 6 Notes Lines and Angles

Updated on 23 Apr 2025, 11:40 AM IST

The chapter Lines and Angles provides the first introduction to geometrical fundamentals. The chapter investigates basic geometric elements that start with points and lines, and rays and continues to explain angle varieties produced by transversal intersections or cuts of lines. Basic geometric understanding depends on these core concepts for learning advanced mathematical shapes that appear later in the textbook.

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NCERT Notes Class 9 Maths Chapter 6 Lines and Angles
Basic Terms and Definitions
Class 9 Chapter Wise Notes
NCERT Solutions for Class 9
NCERT Exemplar Solutions for Class 9
NCERT Books and Syllabus

Lines and Angles

The chapter covers four angle types - acute, right, obtuse, and straight - combined with complementary, supplementary, adjacent and vertically opposite angle pairs. The study of lines intersecting with transversals results in the evaluation of corresponding angles and alternate interior angles, along with other angle properties. All advanced geometry studies require a fundamental understanding of these concepts. Students should utilise the NCERT class 9th maths notes to learn and review various concepts, while using the NCERT notes for supplementary notes on higher-level chapters if needed.

NCERT Notes Class 9 Maths Chapter 6 Lines and Angles

Basic Terms and Definitions

Line Segment:

A portion of the line with two endpoints is called a line segment. It is denoted by the symbol $\overline{AB}$.

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Ray:

A part of the line with one endpoint and the other endpoint extending up to infinity. It is denoted by the symbol $\overrightarrow{AB}$.

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Collinear Points:

If three or more points lie on the same line, they are called collinear points.

Non-Collinear Points:

If three or more points do not lie on the same line, they are called non-collinear points.

Angle:

An angle is generated when two rays originate from the same point. The rays making an angle are called the arms of the angle, while the vertex refers to the place where they end.

Types of Angles:

In geometry, there are several types of angles. The fundamental component of geometry in Mathematics is the angles.

Acute Angle: Measures greater than 0° and less than 90°. It means acute angles are when: 0° < angle < 90°.
Right Angle: Measures equal to 90°. It means right angles are when: Angle = 90°.
Obtuse Angle: Measures greater than 90° and less than 180°. It means obtuse angles are when: 90° < angle < 180°.
Straight Angle: Measures equal to 180°. It means straight angles are when: Angle = 180°.
Reflex Angle: Measures greater than 180° and less than 360°. It means reflex angles are when: 180° < angle < 360°.

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Complementary Angles:

When the sum of two angles is 90°, they form up complementary angle.

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Supplementary Angles:

When the sum of two angles is 180°, they form up supplementary angle.

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Adjacent Angles:

If angles have a common vertex, a common arm, and their non-common arms are on different sides of the common arm, they are called adjacent angles.

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Linear pair of angles:

A pair of adjacent angles whose non-common sides create a straight line that adds up to 180°.

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Vertical Opposite angles:

If two lines intersect each other at a point, they form vertically opposite angles which are equal to each other. Like in the given figure, angles a and c, b and d are vertically opposite angles.

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Intersecting Lines:

When the lines cross each other at a single point, they are called Intersecting lines.

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Non-Intersecting Lines:

When the lines are parallel to each other, or do not intersect, they are called non-intersecting lines.

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Pair of Angles Axioms:

Axiom - Linear Pair of Angles:

If a ray stands on a line, then the sum of two adjacent angles so formed is 180°.

Axiom - Converse of Linear Pair of Angles:

If the sum of two adjacent angles is 180°, then the non-common arms of the angles form a line.

Vertically Opposite Angles Theorem:

If two lines intersect each other, then the vertically opposite angles are equal.

Parallel lines with a Transversal:

A transversal defines a line which crosses different lines at different points. Like in the figure, t is the transversal line.

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Corresponding angles axiom:

When a transversal intersects two parallel lines, then the Corresponding Angles are Equal.

Converse of the Corresponding Angles Axiom:

When a transversal line intersects two lines and the Corresponding Angles are equal, then the lines are parallel to each other.

Alternate Interior Angle Axiom:

When a transversal intersects two parallel lines, then the pair of alternate interior angles is equal.

Converse of Alternate Interior Angle Axiom:

When a transversal line intersects two lines and the alternate interior angles are equal, then the lines are parallel to each other.

The Sum of the Co-interior Angles is Supplementary Axiom:

When a transversal intersects two parallel lines, then the pair of interior angles on the same side of the transversal line are supplementary, i.e. equal to 180°.

The Converse of the sum of the Co-interior angles is supplementary Axiom:

When a transversal line intersects two lines and the interior angles on the same side of the transversal line are supplementary, then the lines are parallel to each other.

Class 9 Chapter Wise Notes

Students must download the notes below for each chapter to ace the topics.

NCERT Notes Class 9 Maths Chapter 1 - Number System

NCERT Notes Class 9 Maths Chapter 2 - Polynomials

NCERT Notes Class 9 Maths Chapter 3 - Coordinate Geometry

NCERT Notes Class 9 Maths Chapter 4 - Linear Equation in Two Variables

NCERT Notes Class 9 Maths Chapter 5 - Introduction To Euclid’s Geometry

NCERT Notes Class 9 Maths Chapter 6 - Lines and Angles

NCERT Notes Class 9 Maths Chapter 7 - Triangles

NCERT Notes Class 9 Maths Chapter 8 - Quadrilaterals

NCERT Notes Class 9 Maths Chapter 9 - Circles

NCERT Notes Class 9 Maths Chapter 10 - Heron's Formula

NCERT Notes Class 9 Maths Chapter 11 - Surface Areas and Volumes

NCERT Notes Class 9 Maths Chapter 12 - Statistics

NCERT Solutions for Class 9

Students must check the NCERT solutions for Class 10 Maths and Science given below:

NCERT Exemplar Solutions for Class 9

Students must check the NCERT exemplar solutions for Class 10 Maths and Science given below:

NCERT Books and Syllabus

To learn about the NCERT books and syllabus, read the following articles and get a direct link to download them.

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2.45×10⁻³ kg

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