Theorem 6.2 Class 9 Maths Explanation with proof

 Theorem 6.2 Class 9 Maths Explanation

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

Theorem 6.2 Class 9 Maths

If a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.

Given

AB ||CD and a transversal r cut AB at P and CD at Q and make two pairs of alternate interior angles(∠3,∠5 ) and (∠4,∠6)

To prove : 

    

∠3= ∠5 and ∠4= ∠6

 

Proof

We have

∠1= ∠3    vertically opposite angles ……..(1)

 and ∠1= ∠5  corresponding angles ……..(2)

From equations (1) and (2),

∠3= ∠5

Again ∠2= ∠4     vertically opposite angles ……..(3)

And ∠2= ∠6   corresponding angles ……..(4)

From equations (3) and (4),

∠4= ∠6

Hence ∠3= ∠5 and ∠4= ∠6

Hence proved

Watch Video to Understand the theorem 6.2 Class 9 Maths

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Related Topics for You

1.    Next theorem – Theorem 6.3 Class 9 Maths

2.    Previous theorem – Theorem 6.1 Class 9 Maths

3.     NCERT Solution of Exercise  6.2