Theorem 6.6 Class 9 Maths Explanation with Proof

Theorem 6.6 Class 9 Maths Explanation with Proof

In this post, we will discuss theorem 6.6 class 9 Maths which is related to Chapter 6 Lines and Angles Class 9 Mathematics. After understanding theorem 6.6, you can solve the exercise questions given in the NCERT book of Class 9 Maths.

Theorem 6.6 Class 9 Maths

Lines which are parallel to the same line, are parallel to each other.

To prove

l∥m

 

Construction: Draw a transversal r cutting l, m, and n at points P, Q, and R respectively.

Proof

Since parallel lines, l and n are intersected by the transversal r at points P and R respectively.

∠1=∠3 (corresponding angles axiom)…..(i)

Again, parallel lines m and n are intersected by the transversal r at points Q and R respectively.

∠2=∠3 (corresponding angles axiom)…..(ii)

From equations (i) and (ii) , ∠1=∠2

But these are corresponding angles 

∴l∥m (by the converse of corresponding angles axiom)

Hence proved

Related Topics for You

1.    Next theorem – Theorem 6.7 Class 9 Maths

2.    Previous theorem – Theorem 6.5 Class 9 Maths

3.     NCERT Solution of Exercise  6.2