Given 3 slopes of 3 lines in which all three wont intersect at the same point. How can we determine whether a triangle can be formed or not? For example
The angles made by the $3$ lines are $50$, $90$, $20$ with $x$ axis.
How can we prove mathematically that they can form a triangle?
Actually I'm writing a program that takes n slopes as input and prints the no. of triangles that can be formed with them. so, in a mathematical way I have asked this question.
 A: This generally depends on the relative position of the lines but if we force two of them intersect at origin the 3rd one shouldn't be concurrent with the two others i.e. if two lines with angles $20$ and $50$ intersect at origin the other one with angle being 90 should be of form$$x=a\quad,\quad a\ne 0$$Another way to saying that is: if the slopes are distinct i.e. all three angles are in the interval $\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)$ and distinct, knowing that this lines aren't concurrent they always form a triangle.
A: The information about the angles tells us that none of the lines is parallel to another. 
It could be the case that the three lines intersect at a single point, and in that case there is no triangle. 
If the three lines do not intersect at a point, call the lines $L_1,L_2,L_3$. Let $A$ be the intersection of $L_1$ and $L_2$, and $B$ the intersection of $L_1$ and $L_3$. We cannot have $A=B$ by our assumption. Since $L_2$ and $L_3$ are not parallel, they intersect at a point $C$. We cannot have $C=A$ or $C=B$ because again we would have a triple intersection. So $ABC$ is a triangle formed by the three lines. 
