Lines and Angles Cass 9 Maths Online solutions

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In this article, we will learn about the theorem based on the below axioms.

Theorem 1.

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.

Theorem 1.2

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

We will draw line t transversal for the lines l,m, and n.

It is already given to us that line m is parallel to the line l and line n is parallel to line l

9th Class Maths - Chapter 6 Lines and Angles Maths NCERT Solutions Class 9, class 9 maths

So it implies

<1=<2 and <1=<3 (using the corresponding angles axiom

So <2=<3

As the < 2 and <3 are corresponding angles and are equal.

Hence with above discussion, we can conclude

Line m is parallel line n.

Hence proved.

Using the Converse of corresponding angles axiom.

The above theorem also states true for more than two lines also.

Theorem 6.3

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

<PQA=<QRC (corresponding angle axiom) equation (i)

<PQA=<BQR equation (ii)

From equ (i) and equ (ii) we can conclude

<BQR=<QRC

<AQR=<QRD

So, from the above, we can conclude that

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

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