## 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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