Two straight lines are parallel to the same third line; prove that they are parallel to each other also.

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Solution

$L e t l i n e s C D & E F b e p a r a l l e l t o t h e s a m e l i n e A B . N o w f r o m t h e l i n e C D b e i n g p a r a l l e l t o A B, i t f o l l o w s t h a t e v e r y p o i n t i n t h e l i n e C D m u s t b e e q u i d i s t a n t f r o m t h e l i n e A B . A n d a l s o l i n e E F b e i n g p a r a l l e l t o A B, i t f o l l o w s t h a t e v e r y p o i n t i n t h e l i n e E F m u s t b e e q u i d i s t a n t f r o m t h e l i n e A B . T h e r e f o r e t h e w h o l e d i s t a n c e s b e t w e e n t h e l i n e C D & E F m u s t b e e q u a l . S o l i n e s C D & E F m u s t b e e q u i d i s t a n t t o e a c h o t h e r & c o n s e q u e n t l y b e p a r a l l e l t o e a c h o t h e r .$

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