NCERT Class 9 Maths Chapter 6 Notes Lines and Angles - Download PDF

# NCERT Class 9 Maths Chapter 6 Notes Lines and Angles - Download PDF

Edited By Ramraj Saini | Updated on Mar 18, 2024 12:36 PM IST

Lines and Angles is the NCERT chapter that deals with different types of angles and their properties. The NCERT Class 9 Maths Chapter 6 Notes covers a brief outline of chapter 6. The main topics covered Lines and Angles class 9 notes, transverse angles, alternative angles, angle sum property of a triangle. Class 9 maths chapter 6 notes also cover the basic equations in the chapter. Lines and Angles class 9 notes pdf download contains all of these topics. The relevant derivations are not addressed in the CBSE class 9 maths chapter 6 notes.

Also, students can refer,

## NCERT Class 9 Maths Chapter 6 Notes Lines and Angles:

Basic Terms And Definitions

1. Point - A Point has no component. It is represented by a dot.

2. Line - When we join two distinct points then we get a line. A line can be extended infinitely.

3. Line Segment - A part of the line which has two endpoints.

4. Ray - Part of the line which has only one endpoint and has no end on the other side.

 Term Dimensions Symbol Point Zero .A Line segment One Ray One Line One

5. Collinear And Non-Collinear Points – Points that lie on the same line are collinear points and the points that don't lie on the same line are Non-Collinear Points.

## Angles

When two rays emerge from a single endpoint then they form an Angle. The two rays are arms of the angle and the endpoint is the vertex of the angle.

### Types of Angles

 Angle Notation Image Acute Angle which is between 0° and 90°. Right Angle which is exactly equal to 90°. Obtuse Angle that is between 90° and 180°. Reflex Angle that is between 180° and 360° Straight Angle that is exactly equal to 180°. Complete Angle that is exactly equal to 360°.

## Complementary And Supplementary Angles

Complementary Angles have the sum of two angles as 90°.

Supplementary Angles have the sum of two angles as 180°.

## Relation Between Two Angles

 Angles Relation Image Adjacent Angles In case two angles have the same vertex and one of the arms is common then these are adjacent angles. Linear pair of Angles In case two angles have the same vertex and one common arm but the arms which are not common make a line, then these are linear pairs of angles. Vertically opposite Angles In case two lines intersect each other at a point, then the opposite angles are vertically opposite angles.

## Intersecting Lines And Non-Intersecting Lines

There are two ways to draw two lines-

1. The lines which cross each other at a particular point are Intersecting Lines.

2. The lines which never cross each other at any point are Non-intersecting Lines. These lines are Parallel Lines and the common length between two lines is the distance between parallel lines.

## Pairs of Angles Axioms

1. If a ray is on a line, then the sum of two adjacent angles formed by the same ray is 180°.

2. If the sum of two adjacent angles is 180°, then the arms which are not common of the angles form a line.

This is the reverse of the first axiom.

## Vertically Opposite Angles Theorem

When two lines intersect each other then the vertically opposite angles formed are equal.

∠AOC = ∠BOD and ∠AOD = ∠COB

## Parallel Lines And A Transversal

When a line passes through two distinct lines and intersects them at different points then this line is called Transversal Line.

Here line “l” is a transversal of the lines m and n.

Exterior Angles are - ∠1, ∠2, ∠7 and ∠8

Interior Angles are - ∠3, ∠4, ∠5 and ∠6

1. Corresponding Angles :

• ∠1 and ∠6

• ∠2 and ∠5

• ∠4 and ∠7

• ∠3 and ∠8

2. Alternate Interior Angles :

• ∠3 and ∠6

• ∠4 and ∠5

3. Alternate Exterior Angles:

• ∠2 and ∠7

• ∠1 and ∠8

4. Interior Angles on the same side of the transversal:

• ∠3 and ∠5

• ∠4 and ∠6

## Transversal Axioms

1. When a transversal intersects two parallel lines, then

• The pair of corresponding angles will be equal.

• The pair of alternate interior angles will be equal.

• Pair of interior angles on the same side of the transversal will be supplementary.

2. If a transversal intersects two lines in a way that

• Corresponding angles are equal then these two lines are parallel to each other.

• Alternate interior angles are equal then the two lines are parallel.

• Interior angles on the same side of the transversal are supplementary than the two lines are parallel.

## Angle Sum Property of A Triangle

1. The sum of angles of a triangle is 180º.

2. If from any side of a triangle, then the exterior angle formed is equal to the sum of two interior opposite angles.

∠ACD = ∠ABC + ∠BAC

## Significance of NCERT class 9 maths chapter 6 notes

• Lines and Angles class 9th notes will give a detailed overview of the chapter and get a sense of the main topics discussed.
• These notes explain math stuff in a simple way, making it easier for you to get what's going on.
• They cover all the basic math concepts you need to know. This sets you up nicely for more advanced math in the future.
• Follows Your School Syllabus: The notes match exactly what your school teaches, so you're always on track with what you're supposed to learn.
• You get plenty of practice problems to try out. This helps you get better at solving math questions step by step.
• This NCERT class 9 maths chapter 6 notes is also useful for covering the core themes of the CBSE maths syllabus in class 9 as well as for competitive exams such as VITEEE, BITSAT, JEE Main, NEET , and others.
• In offline mode, Class 9 maths chapter 6 notes pdf download can be used to prepare.

NCERT Class 9 Notes Chapter wise

 NCERT Class 9th Math Chapter 1 Notes NCERT Class 9th Maths Chapter 2 Notes NCERT Class 9th Maths Chapter 3 Notes NCERT Class 9th Maths Chapter 4 Notes NCERT Class 9th Maths Chapter 5 Notes NCERT Class 9th Maths Chapter 6 Notes NCERT Class 9th Maths Chapter 7 Notes NCERT Class 9th Maths Chapter 8 Notes NCERT Class 9th Maths Chapter 9 Notes NCERT Class 9th Maths Chapter 10 Notes NCERT Class 9th Maths Chapter 11 Notes NCERT Class 9th Maths Chapter 12 Notes NCERT Class 9th Maths Chapter 13 Notes NCERT Class 9th Maths Chapter 14 Notes NCERT Class 9th Maths Chapter 15 Notes

NCERT solutions of class 9 subject wise

NCERT Class 9 Exemplar Solutions for Other Subjects:

1. Are all the main derivations covered in the class class 9 maths chapter 6 notes?

N0, all the main derivations are not covered in the NCERT notes for class 9 maths chapter 6. This NCERT note is a brief of the main topics and equations covered in the chapter and can be used for revising the Lines and Angles.

2. How important is the chapter for the CBSE board exam and how this class 9th maths chapter 6 notes would help?

Students can expect 4 to 8 marks questions from the notes for class 9 maths chapter 6 and students can refer to this note for the quick revision purpose which would help them to increase their marks.

3. State angle sum property of a triangle.

As mentioned in class 9 Lines and Angles notes, the sum of all the angles of a triangle is 180˚.

4. What are complementary angles?

It is mentioned in, class 9 maths chapter 6 notes pdf download that Complementary Angles have the sum of two angles as 90°.

5. What are supplementary angles ?

Supplementary Angles have the sum of two angles as 180° is stated in Lines and Angles class 9 notes pdf download.

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