Theorem 6.3 Class 9 Maths Explanation with Proof

Theorem 6.3 Class 9 Maths Explanation with Proof

In this post, we will discuss theorem 6.3 class 9 Maths which is related to Chapter 6 Lines and Angles Class 9 Mathematics. After understanding theorem 6.3, you can solve the exercise questions given in the NCERT book of Class 9 Maths.

Theorem 6.3 Class 9 Maths

If a transversal intersects two lines, such that a pair of alternative interior angles are equal, then the two lines are parallel.

Given

A transversal r intersects two lines Ab and CD at points P and Q, respectively such that 

         ∠3=∠5

and  ∠4=∠6

To prove :

AB is parallel to CD AB||CD

 

Proof:

We have 

         ∠3=∠5    (alternate interior angles)…………(i)

And ∠3=∠1     (vertically opposite angles)………(ii)

Then, from equations (i) and (ii)

∠1=∠5

But these are corresponding angles 

So AB||CD (by the converse of corresponding angles axion)

Hence proved

Related Topics for You

1.    Next theorem – Theorem 6.4 Class 9 Maths

2.    Previous theorem – Theorem 6.2 Class 9 Maths

3.     NCERT Solution of Exercise  6.2