Proposition 13

This proposition states that when a ray extends out of a line, then the sum of the angles it forms is equal to two right angles. The two angles formed are often called supplementary. This statement sounds obvious even in the weirdest of geometries, so it makes sense that its proof would be pretty simple. First, a line segment BE is constructed perpendicular to CD. We can then break up the yellow angle plus the red angle as the angle DBE plus EBA, plus the red angle, and regrouping reveals that this is just twice angle DBE, or two right angles.