What is the difference between plane and spherical triangles?

Answer 1

The difference between plane and spherical triangles is that plane triangles are constructed on a plane, and spherical triangles are constructed on the surface of a sphere. Let's take one example and run with it. Picture an equilateral triangle drawn on a plane. It has sides of equal length (naturally), and its interior angles are each 60 degrees (of course), and they sum to 180 degrees (like any and every other triangle). Now, let's take a sphere and construct that equilateral triangle on its surface. Picture an "equator" on a sphere, and cut that ball in half through the middle. Set the top half on a flat surface and cut it into four equal pieces. Now if you "peel up" the surface of one of those quarters and inspect that triangle, it will have three sides of equal length, and will have three right angles. Not possible on a plane, but easy as pie on the surface of a sphere. Spherical trig is the "next step up" from plane trig.