Does a Scalene Triangle Exist? Proving Its Existence with a Simple Construction

[dancergirlie]

Homework Statement

Prove that a scalene triangle exists

Homework Equations

The Attempt at a Solution

I really don't know how to approach this proof... should I do a direct proof or maybe by contradiction? Any help would be great...

 

[LCKurtz]

The easiest way to show something exists is to demonstrate one. So pick three points in the xy plane that give vertices of a scalene triangle and then verify it is.