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

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Solution

$\begin{matrix} \Rightarrow A B ∥ E F a n d \Rightarrow C D ∥ E F t o p r o v e A B ∥ C D \Rightarrow ∠ 1 = ∠ 3 (c o r r e s p o n d i n g a n g l e s) \Rightarrow C D ∥ E F \Rightarrow ∠ 2 = ∠ 3 (c o r r e s p o n d i n g a n g l e s) \Rightarrow ∠ 1 = ∠ 2 h e n c e A B ∥ C D \end{matrix}$

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