# NCERT solutions for class 9 Lines and Angles Chapter 6 ## NCERT solutions for class 9 Lines and Angles Chapter 6

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In this article, we will learn the properties of the angle formed when two lines intersect each other and also the properties of the angle formed when a line intersects two or more parallel lines at distinct points.

Class 9 Maths – Basic terms and definition

• Line segment- A portion of line with two end points
• Ray- A line with one end point
• Collinear points- If three or more points lie on the same line they are called collinear points
• Angle- An angle is formed when two rays originate from the same end points.
• Arm- The rays, making an angle are called the arms
• Vertex- The end points of the rays making an angle are called vertex
• Acute angle- An angle that measures between 0⁰ to 90⁰.
• Right angle- An angle equal to 90⁰.
• Obtuse angle- An angle greater than 90⁰. but less than 180⁰.
• A straight angle- is equal to 180⁰.
• Reflex angle- an angle which is greater than 180⁰ but less than 360⁰ is called the reflex
• Complementary angle Two angles whose sum is 90⁰.
• Supplementary anglesTwo angles whose sum is 180⁰.
• Linear pair of angles- When the sum of two adjacent angles is 180⁰, they are called a linear pair of angles.

Linear pair axiom

If a ray stands on a line, then the sum of the two adjacent angles so formed is 180⁰ and vice Vera. This property is called as the linear pair axiom

• If a ray stands on a line, then the sum of two adjacent angles so formed is 180⁰.
• If the sum of two adjacent angles is 180⁰ than the non-common arms of the angles from a line.

As per Class 9 Maths syllabus, we will now discuss few theorems:

Theorem 1:-If two lines intersect each other than the vertically opposite angles are equal

Given: – AB and CD are two intersecting lines at O. Two vertically opposite angles as below

1. <AOC and <BOD
2. <AOD and <BOC To prove:-<AOC=<BOD and <AOD -<BOC

Proof:– Ray OA stands on line CD

Therefore <AOC+<AOD=180⁰ (linear pair axiom) equation 1

<AOD+<BOD=180⁰   equation 2

From equation 1 and equation 2

=<AOC+<AOD=<AOD+<BOD

=this implies that <AOC=<BOD

Hence proved.

Same way, we can also prove that <AOD=<BOC.

In the Class 9 Maths Solutions, next article, we will discuss parallel lines and the transversal theorems, lines parallel to the same line theorems. Keep watching the space for more.

For an animated explanation of the topic with examples, click 9 class maths video classes, class 9 maths NCERT solutions. And for more classes and courses, register with Takshila Learning.

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