Maximum and minimum triangle angle sum in non-euclidian geometry

[Dheglen]

So, I called my mother and told her that I was trying to construct a triangle with two right angles, and she said "that it's not possible". I said "yes it is", she said "no it isn't" etc...

Anyway, is the maximum angle sum 90 * 3 = 270 degrees, and the minimum close to zero?

 

[MathLover1]

Can a triangle have two right angles? The answer is “NO” in Euclidian Geometry., a triangle can never have two right angles. Reason: Sum of the three interior angles of a triangle must be 180 degrees.

but spherical geometry you can have two or even three :

 

[Dheglen]

Can a triangle have two right angles? The answer is “NO” in Euclidian Geometry., a triangle can never have two right angles. Reason: Sum of the three interior angles of a triangle must be 180 degrees.

And an angle can't be 0 degrees?

 

[MathLover1]

in Euclidian Geometry
The key reason that triangles cannot have angles which measure 0° is that such a figure would necessarily be 3 points on a straight line, and such a figure is not a triangle.

 

[nycmathguy]

So, I called my mother and told her that I was trying to construct a triangle with two right angles, and she said "that it's not possible". I said "yes it is", she said "no it isn't" etc...

Anyway, is the maximum angle sum 90 * 3 = 270 degrees, and the minimum close to zero?

So, I called my mother and told her that I was trying to construct a triangle with two right angles, and she said "that it's not possible". I said "yes it is", she said "no it isn't" etc...

Anyway, is the maximum angle sum 90 * 3 = 270 degrees, and the minimum close to zero?

This question should be asked in the Other Advanced Math forum. The Geometry and Trigonometry forum is more for high school and undergraduate mathematics.

 

[nycmathguy]

Can a triangle have two right angles? The answer is “NO” in Euclidian Geometry., a triangle can never have two right angles. Reason: Sum of the three interior angles of a triangle must be 180 degrees.

but spherical geometry you can have two or even three :

Is this not geometry beyond the high school and undergraduate level of mathematics? This question should be posted in the Other Advanced Math forum. Agree?

 

[Dheglen]

in Euclidian Geometry
The key reason that triangles cannot have angles which measure 0° is that such a figure would necessarily be 3 points on a straight line, and such a figure is not a triangle.

Does it have to have an area > 0 to be a triangle?

 

[MathLover1]

yes
Any figure with 0 square with area is not possible.