Sarthaks Test
0 votes
161 views
in Mathematics by (15.0k points)

Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.

1 Answer

0 votes
by (24.8k points)
selected by
 
Best answer

Yes.

According to Euclid’s 5th postulate, when n line falls on l and m and if ∠1 + ∠2 < 180°, then ∠3 + ∠4 > 180°producing line l and m further will meet in the side of ∠1 and ∠2 which is less than 180°.

The lines l and m neither meet at the side of ∠1 and ∠2 nor at the side of ∠3 and ∠4. This means that the lines l and m will never intersect each other. Therefore, it can be said that the lines are parallel.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...