एक ही रेखा के समानांतर रेखाएँ

Fig. 1 - Transversal Line

If two lines are parallel to the same line, will they be parallel to each other? Let us verify.

In the fig.1 line $m||$ line $l$ and line $n||$ line $l$ .

Let us draw a line $t$ transversal for the lines $l,m,n$

We know that line $m||$ line $l$ and line $n||$ line $l$ .

Hence $\angle 1=\angle 2$ and $\angle 1=\angle 3$ (Corresponding angles axiom)

But $\angle 2=\angle 3$ as they are corresponding angles

Therefore, we can say that line $m||$ line $n$ (Converse of corresponding angles axiom)

This result can be stated in the form of the following theorem:

Theorem 1: Lines which are parallel to the same line are parallel to each other.