Final answer:
The sum of all angles in a triangle adding up to 180 degrees is a basic feature of Euclidean geometry, distinct from the Pythagorean theorem, which relates to right-angled triangles.
C. A Property of Euclidean Geometry.
Step-by-step explanation:
The sum of all angles in a triangle adding up to 180 degrees is a fundamental property of Euclidean geometry. This is unrelated to the Pythagorean theorem, which specifically concerns the relationship between the sides of a right-angled triangle (a2 + b2 = c2). Rather, the fact that triangle angles sum up to 180 degrees comes from the parallels postulate, which implies, through alternate interior angles, that the sum of angles in any triangle in flat space will always equal 180 degrees. When one extends a side of the triangle, the exterior angle formed is equal to the sum of the opposite interior angles, and since this exterior angle is also formed by a straight line, which measures 180 degrees, it logically follows that the interior angles must add up to 180 degrees as well.
Therefore, the correct answer to the question is C. A Property of Euclidean Geometry. The other options (Pythagorean Theorem, Law of Cosines, and Internal Forces) are not directly related to the fundamental geometric property that the sum of angles in a triangle equals 180 degrees.