I believe the common end points are called vertices. Each separate one is called a vertex, but the plural of "vertex" is "vertices."
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The vertices of a triangle are the endpoints. In other words, when the sides of the triangle intersect, they form a vertex of a triangle. A triangle has a total of three vertices.
-- If both of its endpoints are the same vertex, then the line segment's lengthis zero, and you'd look at it and swear that it was only a point, and you can'tsee it at all if you don't know it's there.-- If each of its endpoints is a different vertex, then the line segment exactlycoincides with one side of the triangle, and you can't see it at all if you don'tknow it's there.
A line
that one!
A Triangle :)