Does Euclid's fifth postulate imply the existence of parallel lines? Explain.
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22
yes it implies the existence of parallel lines.
if one side of the parallel lines are less than 180 degrees they are not paralleland if one side is equal two 180degrees the lines are parallel
hope it helps
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if one side of the parallel lines are less than 180 degrees they are not paralleland if one side is equal two 180degrees the lines are parallel
hope it helps
pls mark as brainliest
Answered by
14
HEY!!
If a straight line falls on two straight lines m and n such that sum of the interior angles on one side of l is two right angles, then by Euclid' s fifth postulate the line will not meet the one side of l. Next, you know that the sum of interior angles on the other side of line l will also be two right angles. Therefore, they will not meet at the other side also. So, the lines m and n will never meet and are therefore parallel.
If a straight line falls on two straight lines m and n such that sum of the interior angles on one side of l is two right angles, then by Euclid' s fifth postulate the line will not meet the one side of l. Next, you know that the sum of interior angles on the other side of line l will also be two right angles. Therefore, they will not meet at the other side also. So, the lines m and n will never meet and are therefore parallel.
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