PROVE THAT THE TWO LINES WHICH ARE BOTH PARALLEL TO THE SAME LINE ARE PARALLEL TO ONE ANOTHER - Maths - Lines and Angles

Question

PROVE THAT THE TWO LINES WHICH ARE BOTH PARALLEL TO THE SAME
LINE ARE PARALLEL TO ONE ANOTHER

Koka Sri Lakshmi Divya Sai · Accepted Answer

$We have three lines l,m and n,it is given l is parallel to m i.e.,l ∥ m and line n is parallel to mi.e., n ∥ m we need to prove that line l is parallel to line n or l ∥ n we draw a transversal line pintersecting lines l,m amd n Since lines l and m are parallel we have ∠ 1 = ∠ 2 (∵ Corresponding angles are equal) - - - - (i) Since lines n and m are parallel we have ∠ 2 = ∠ 3 (∵ Corresponding angles are equal) - - - - (i i) From (i) amd (ii) we get ∠ 1 = ∠ 2 = ∠ 3 \Rightarrow ∠ 1 = ∠ 3 \Rightarrow l ∥ n$

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PROVE THAT THE TWO LINES WHICH ARE BOTH PARALLEL TO THE SAME LINE ARE PARALLEL TO ONE ANOTHER.