Well, choose three points on the sphere. Can we connect them with straight lines (great circles)? Yes, the first axiom tells us that. So triangles do exist -- they are "fat-angled" triangles.

We know the sum of the angles in a triangle is 180 degrees. Is this true in spherical geometry?

For example, draw a triangle on a globe. Put two of the points on the equator and the third point at the North Pole.

What? Three right angles? How could that be?

Yes, the sum of the angles for this triangle is 270 degrees. We could spread the legs of the triangle to get an even bigger sum.

What about a square? Can we draw a square without parallel lines? Hmmm .....

A square is a regular quadrilateral -- four equal sides and four equal angles. Can we draw a regular quadrilateral in spherical geometry?

Draw four lines so that the shape in the center has all sides and all angles the same -- this regular quadrilateral can be called a square by this definition, but does not have the same properties as a square in Euclidean geometry -- the sides are not parallel and the angles are not 90 degrees.