CBSE & NCERT solutions for class 9 Lines and Angles Chapter 6

NCERT solutions for 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 angles–Two 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

<AOC and <BOD
<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.

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