Q. 1

Prove that the follo

Answer :

Suppose that the lines l and k are parallel and line m intersects k at a point.

We will use the playfair form of the Euclidean fifth postulate.


If m does not intersect l, then m is parallel to l.

This would mean that there are two parallels to l through P(m and k). contradicting play fair's axiom.

Thus, m must also intersect l. Now let P be a point and l a line not through P.

we can construct a line parallel to l through P, call it k. Let m be any other line through P.

Since it intersects one of two parallel lines (k), it must intersect the other (l) by assumption. thus, there is only one line through P which is parallel to l.

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