Does Euclid's fifth postulate imply the existence of parallel lines? Explain.
Answers
Answer:
Step-by-step explanation:
The Fifth Postulate
So far everything has been going very well. However these first four postulates are not enough to do the geometry Euclid knew. Something extra was needed. Euclid settled upon the following as his fifth and final postulate:
5. That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles,
the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
It is very clear that there is something quite different about this fifth postulate. The first four were simple assertions that few would be inclined to doubt. Far from being instantly self-evident, the fifth postulate was even hard to read and understand.
5. That, if a straight line falling on two straight lines...
Euclid 5 1
... make the interior angles on the same side less than two right angles... [in this case, side on the right]
Euclid 5 2
...the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Hope it helps you....
Answer:
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