The sum of the angles in a triangle varies according to the geometry in which the triangle lies.

1. Prove that the statement "There exists a triangle with a sum of angles greater than 180 degrees" is true in spherical geometry.

2. Prove that the statement "The sum of the angles in any triangle is 180 degrees" is true in Euclidean geometry.

Note: The attached "Parallel Postulate to Triangles Diagram" may prove useful in relating the parallel postulate to triangles.

3. Prove that the statement, "Rectangles do not exist," is true in hyperbolic geometry.