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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