Theorem 6.1 Class 9 Maths Explanation with Proof

 Theorem 6.1 Class 9 Maths Explanation with Proof

In this post, we will discuss theorem 6.1 class 9 Maths which is related to Chapter 6 Lines and Angles Class 9 Mathematics. After understanding theorem 6.1, you can solve the exercise questions given in the NCERT book of Class 9 Maths. You can also go through theorem 6.2 to understand the complete chapter 6 Lines and angles.

Theorem 6.1Class 9 Maths

If two lines intersect each other, then the vertically opposite angles are equal.

Given

Two lines AB and CD intersect each other at a point O

To prove 

The vertically opposite angles are equal i.e.      i.   ∠AOC= ∠BOD      ii.   ∠AOD= ∠BOC

Vertically Opposite angles

Proof

 (i) Here, ray OC stands in line with AB

∠AOC+ ∠BOC=180°   (by linear pair axiom)…..(i)

Again, ray OB stands on line CD

 ∠BOC + ∠BOD=180°        (by linear pair axiom)…..(ii)

From equations (i) and (ii)

∠AOC+∠BOC=∠BOC+∠BOD

On subtracting ∠BOC  from both sides, we get

  ∠AOC= ∠BOD

(ii) Similarly we can prove that 

   ∠AOD=∠BOC

Hence proved

Related Topics for You

    1.   Next theorem – Theorem 6.2 Class 9 Maths

    

 

Watch Video to Understand the theorem 6.1 Class 9 Maths

Related Topics for You

1.    Next theorem – Theorem 6.2 Class 9 Maths

2.     NCERT Solution of Exercise  6.2

Frequently Asked Questions (FAQ)

1. How theorems of class 9 mathematics subject are helpful in doing questions or sums of maths?

Ans. - Theorems of class 9 mathematics are very helpful in doing questions or sums of maths. you will be able to solve all questions and sums of mathematics in class 9.