A triangle with integer co ordinates and integer sides Is there a triangle with integer sides as well as integer co ordinates when none of the angles is $90$? I tried to solve the general case but I am stuck with it.
Update:
Let the Triangle be $T$ whose vertics are $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ such that $x_i\neq x_j\neq y_i \neq y_j$ and angles such that $A_i\neq \frac{\pi}{2}$

The triangle with vertexes $(-3,0),(3,0),(0,4)$
Note 1: Consider any Pythagorician triple $(a,b,c)$, then $a,b,c \in \mathbb{N}$ and $a^2+b^2=c^2$. Now consider the triangle with vertexes of coordinates $(0,0),(b,0),(0,a)$. Finally to avoid the right angle consider the triangle with vertexes $(-b,0),(b,0),(0,a)$. Clearly all coordinates are integers and $$\|(b,0) - (-b,0)\|=2b, \quad \|(\pm b,0) - (0,a)\| = c,$$
which shows that all the edges have integer lengths.
Note 2: Exploiting the same idea, we may also construct non isosceles triangles. Therefore consider $(a,b,c)$ a Pythagorician triple and $(b,d,e)$ another Pythaforician triple (e.g. $(5,12,13)$ and $(12,35,37)$), then the triangle $(-a,0), (d,0), (0,b)$ has integer side lengths and vertexes coordinates.
