Theorem 6.5 Class 9 Maths Explanation with Proof

Theorem 6.5 Class 9 Maths Explanation with Proof

In this post, we will discuss theorem 6.5 class 9 Maths which is related to Chapter 6 Lines and Angles Class 9 Mathematics. After understanding theorem 6.5, you can solve the exercise questions given in the NCERT book of Class 9 Maths.

Theorem 6.5 Class 9 Maths

If a transversal intersects two lines such that a pair of interior angles on the same side of the transversal is supplementary, then the two lines are parallel.

Given 

A transversal r intersects two lines AB and CD at P and Q, respectively such that ∠3,∠6, and ∠4,∠5  are pairs of interior angles on the same side of r and ∠3+∠6=180°,∠4+∠5=180°.

To prove

AB||CD

 

Proof 

Here, ray PB stands on line r

∴∠2+∠3=180° (by linear pair axiom)……….(i)

  ∠3+∠6=180°      …………………….(ii)

From equations (i) and (ii)

∠2+∠3=∠3+∠6

on subtracting∠3  from both sides, we get   ∠2=∠6

But these are corresponding angles 

So, AB||CD (by the converse of the corresponding angels axiom)

Hence proved

Related Topics for You

1.    Theorem 6.6 Class 9 Maths

2.     Theorem 6.4 Class 9 Maths

3.     NCERT Solution of Exercise  6.2