Final answer:
The triangle angle sum theorem is true on the surface of a cylinder, sphere, and rectangular prism because these shapes can be unfolded into a flat plane.
Step-by-step explanation:
The triangle angle sum theorem states that the sum of the three angles in a triangle is always 180 degrees.
On the surface of a cylinder, sphere, and rectangular prism, the triangle angle sum theorem is still true. The reason is that these shapes can be unfolded into a flat plane, and on that plane, the sum of the angles in a triangle is always 180 degrees. So even though these shapes are three-dimensional, the geometry within them follows the same rules as two-dimensional triangles.