Question

Prove that the two lines which are both parallel to the same line are parallel to each other

Answer 1

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Answer 2

$\huge\mathfrak\orange{\underline{\underline{Solution :-}}}$

Let l be a given line.

Draw two line m and n parallel to the line l,

i.e., m ll l and n lll

Draw a transversal line t for the lines l, m and n.

$\therefore$ $\bf\angle$1= $\bf\angle$2 ....(1) [Corresponding angle s , as l ll m ]

Similarly, $\bf\angle$1= $\bf\angle$3. .....(2)[Corresponding angle s, as l ll n]

From (1) and (2), we have

$\bf\angle$2= $\bf\angle$3

• But $\bf\angle$2 and $\bf\angle$3 are corresponding angles and they are equal.

$\therefore$Line m ll Line n

[converse of corresponding angles axiom.]