What is the theorem that states that a triangle cant be a triangle unless the angles equal 180 degrees?

Question

Specifically the name

Answer 1

[02]
The theorem states that the sum of measures of the three angles of a triangle is always 180 degrees.

Answer 2

YES - in non-planar geometry e.g. spherical trigonometry.
This is one example of a non-Euclidean geometry. (Hyperbolic geometry would be another)

A triangle on the outside of a sphere always has >180deg

"Remarkably, the sum of the vertex angles of a spherical triangle is always larger than the 180° found in every planar triangle. The amount by which the sum of the angles exceeds 180° is called the spherical excess E: E = α + β + γ − 180°. This surplus determines the surface area of any spherical triangle. To determine this, the spherical excess must be expressed in radians; the surface area A is then given in terms of the sphere's radius R by the expression:

A = R^2 · E. From this formula, which is an application of the Gauss-Bonnet theorem, it becomes obvious that there are no similar triangles (triangles with equal angles but different side lengths and area) on a sphere."

Spherical law of cosines:
cos c = cos a cos b + sin a sin b cos C

(A spherical triangle abc is specified as usual by its corner angles a,b,c and its sides A,B,C, but the sides A,B,C are given not by their length, but by their arc angle.)

Answer 3

Its got to have 3 corners to be a triangle and the 3 corners angles has to add up to 180 degrees, if it don't, then its not a triangle.

Answer 4

The sum of the angles of any triangle in plane geometry is exactly 180 degrees.

Answer 5

i'm not really sure if there's a name but the theorem probably came about that a triangle equals 180 degrees b/c it's half a quadrilateral polygon.

Answer 6

I think the Pythoragam Theory