However, by the fith axiom of euclid, the lines in your example cannot be parallel AND converge (not even in infinity). Thus, it's more an open rectangle.
Either they are overlapping which violates the definition of a triangle, or they don't and the parallel lines always maintain the same distance X to each other and consequently maintain distance X at infinity (let's say X=1, bc you can just scale it).
Either they are overlapping which violates the definition of a triangle, or they don't and the parallel lines always maintain the same distance X to each other and consequently maintain distance X at infinity (let's say X=1, bc you can just scale it).