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# CBSE Class 9 Answered

How does Euclid's fifth postulate imply the existence of parallel lines? Give a mathematical proof.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
Expert Answer

Euclid's 5th postulate states that:

If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.

This implies that if n intersects lines l and m and if . In that case, producing line l and m further will meet in the side of1 and 2 which is less than 180o

If

In that case, the lines l and m neither meet at the side of 1 and 2 nor at the side of 3 and 4.

Implying that the lines l and m will never intersect each other.

Therefore, the lines are parallel.

Answered by | 04 Jun, 2014, 03:23: PM

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