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Class 9 maths NCERT solutions - Lines and Angles

Class 9 maths NCERT solutions - Lines and Angles

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.
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.
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