Triangle with no area when c=a+b

Question

I vaguely remember there being some type of "collapsed" triangle in Geometry, that possibly had to do with the area of a circle. Today in class we reviewed Pythagorean theorem, and how $c<a+b$ had to be true in a right triangle. If $c=a+b$, would this be called a collapsed/reduced triangle with zero area? Or is this just a straight line segment with three points?

Answer 1

If $c=a+b$, you would simply view it as a line (segment).

The conditions to satisfy a triangle with some area, the sides $c<a+b$, $b<a+c$, and $a<b+c$.

Two of the three points of the triangle $A$, $B$, $C$, would be stacked on top of one another, so either Point $A$ would be in the same position as point $B$, Point $B$ would be in the same position as point $C$, or Point $A$ would be in the same position as point $C$.