Answer :

Suppose that the lines

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

If

This would mean that there are two parallels to

Thus,

we can construct a line parallel to

Since it intersects one of two parallel 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.*Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

Related Videos

Polynomials- Introduction45 mins

Prepositions43 mins

NIST Rules to Write Units30 mins

Questions based on Acceleration due to Gravity40 mins

Nouns and Pronouns48 mins

Verb and Tenses48 mins

Adjectives and Adverbs43 mins

Conjunctions43 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation