Euclid's fifth postulate

Here is a possible proof of Euclid's 5th postulate Suppose that the two lines meet on the other side i.e. not on the side where sum of interior angles on the same side of transversal is less than 180 degrees. This will force the sum of angles of the triangle formed to be greater than 180 degrees which is not possible. So lines must meet on the opposite side where sum of interior angles on the same side of transversal is less than 180 degrees. what is wrong ?

Note by Kumar Saurav
5 years, 10 months ago

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How do you prove that sum of angles of a triangle is 180. In that proof You used the idea that a line parallel to another line can be constructed from any other point ( apart from one on the original line itself) So this statement is another equivalent to the 5 th axiom So since you already used an equivalent of the 5th axiom to prove that property u cannot use it again to prove the axiom. Therein lies the mistake of your proof

- 5 years, 10 months ago

Non euclidean geometry with hyperbolic,spherical triangles and fractals,right ?

- 5 years, 10 months ago

As Pranav says.....................it's true that you have used the 5th axiom and thus it no longer remains correct.

- 5 years, 10 months ago

How will you prove that the other side will have sum of angles grater than 180 ? Nice try chum using contradiction. But no one yet has been able to prove this postulate with other 4 axioms .

Fact to know : While trying to prove this postulate using the 4 axioms , non-euclidean geometry was developed !

- 5 years, 10 months ago

Nice try............

- 5 years, 10 months ago

Don't understand. :(

- 5 years, 10 months ago

proof for sum of of angles of triangle uses alternate interior angles theorem which is derived from corresponding angles theorem

- 5 years, 10 months ago