Let's recall the definition of a line in spherical geometry.
A line is a circle on the sphere whose diameter is equal to the diameter of the sphere.
With the above definition, we can draw a sphere and a line in spherical geometry.
Can we draw two parallel lines in a sphere? No, we cannot. The reason is that this line would have to be offset either up or down to be parallel, and therefore it will not have the same diameter as the sphere.
This means it would not meet the definition of a line in spherical geometry anymore. Therefore, since we cannot have parallel lines in a sphere, we cannot have a transversal that intersects two parallel lines.
