Spherical Geometry and Proposition 16
Proposition 16
In any triangle, if one of the sides is produced, then the exterior angle is greater than either of the interior and opposite angles.
Proposition 16 Disproof
Proposition 16 Disproof
To show that proposition 16 fails in spherical geometry, we need to show a counter example. As we have discussed in class, you can have triangles in spherical geometry where you can have multiple angles greater than or equal to a right angle(for example the applet above). The proportion says that on any side if one of the angles is produced, it will be greater than both the interior and opposite angles. If we produce one of the sides of the triangle above, the exterior angle will be another right angle. Since all angles are equal to a right angle as well, the exterior angle is not greater than either of the interior and opposite angles. Therefore we have found an example of a triangle that fails proposition 16.