#### notes

If two lines are parallel to the same line, will they be parallel to each other in following fig.

Line m || line l and line n || line l.

Let us draw a line t transversal for the lines, l, m and n. It is given that line m || line l and line n || line l.

Therefore, ∠ 1 = ∠ 2 and ∠ 1 = ∠ 3

(Corresponding angles axiom)

So, ∠ 2 = ∠ 3

But ∠ 2 and ∠ 3 are corresponding angles and they are equal.

Therefore, you can say that

Line m || Line n

(Converse of corresponding angles axiom)

#### theorem

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

Note : The property above can be extended to more than two lines also.

Now, let us solve some examples related to parallel lines.

#### Shaalaa.com | Theorem: Lines which are parallel to the same line are parallel to each other.

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