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  • Write whether the following statements are True or False? Justify your answer: “For every line l and for every point P not lying on a given line, there exists a unique line m passing through P and parallel to l is known as Playfair’s axiom.”

Write whether the following statements are True or False? Justify your answer:

“For every line l and for every point P not lying on a given line, there exists a unique line m passing through P and parallel to l is known as Playfair’s axiom.”

Answers (1)

True

Solution:

Euclid’s fifth postulate: according to Euclid’s fifth postulate if two lines are drawn which intersect a third line in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other.  So according to Euclid’s fifth postulate, it is true that a line m can pass from point p with parallel to line l.

Playfair's axiom: Given a line in a plane, and a point not on this line. At most one line parallel to the given line can be drawn through the point. So Playfair's axiom is an axiom which can be used instead of the fifth postulate of Euclid.

Hence the given statement is true.

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infoexpert24

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