Class 9 Maths Solutions Chapter 6- Lines and Angles
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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
=this implies that <AOC=<BOD
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.