Prove that two distinct lines cannot have more than one point in common.

Asked by kousikroyr20 | 10th Sep, 2015, 11:42: PM

Expert Answer:

S u p p o s e space o n space t h e space c o n t r a r y space t h a t space t w o space d i s t i n c t space l i n e s space a r e space h a v i n g space t w o space p o i n t s space i n space c o m m o n comma space P space a n d space Q. S o space t h e r e space a r e space t w o space d i s t i n c t space l i n e s space p a s sin g space t h r o u g h space P space a n d space Q. B u t space b y space E u c l i d apostrophe s space p o s t u l a t e comma space o n l y space o n e space l i n e space c a n space b e space d r a w n space t h r o u g h space t w o space d i s t i n c t space p o i n t s. T h i s space c o n t r a d i c t s space o u r space a s s u m p t i o n space a n d space h e n c e space o u r space a s s u m p t i o n space i s space w r o n g. T h u s comma space t h e space t w o space d i s t i n c t space l i n e s space c a n n o t space h a v e space m o r e space t h a n space o n e space p o i n t space i n space c o m m o n.

Answered by Vimala Ramamurthy | 11th Sep, 2015, 11:23: AM