I thought that was a fairly interesting statement. If I was a student, I would want my professor to state things like this. Liekwise, if I was a professor, I would introduce things like this to my class.
Theorems and Postulates for Geometry
I was messing with the triangle on the interactive thing, and made the triangle just a line. It said the line is an obtuse isosceles triangle. Really? Is "obtuse isosceles triangle" really another way to say "a line"?
Edit: I was thinking about this and I think the definition of triangle should be (if it's not already) a shape with 3 angles, each greater than 0.
I haven't used this tool, so I can't check what you were looking at. However, in mathematics you will find many examples of what are called "degenerate" forms of familiar objects. Yes, you can flatten a triangle into a straight line and it is still technically a triangle. You can also squash a cube into a flat plane and you can do many other strange things. When first learning the subject, these special cases are just confusing so teachers avoid them. However, they turn out to be important further on in mathematics so it is useful to get comfortable with degenerate cases of geometric and algebraic objects.
There is also a very good site about geometry:gogeometry.com .the site contains a big number of theoremes as exercises with many question in order to prove the theoreme,
Why would you want that to be the definition? There is nothing inconsistent or wrong about a degenerate triangle like the one you describe.
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