Property #3
4. Adding Up to 180 Degrees
Alright, one more angle adventure, and then we can all go have a geometry-themed party (just kidding… unless?). We’re still using our trusty transversal cutting across parallel lines. This time, we’re focusing on angles that are inside the parallel lines and on the same side of the transversal. These are called same-side interior angles, also sometimes called consecutive interior angles.
Here’s the key difference from the previous properties: these angles are not congruent. Instead, they are supplementary. What does supplementary mean? It means that when you add their measures together, you get 180 degrees. That’s half a circle, a straight line, or, in other words, a flat angle.
So, picture one same-side interior angle being, say, 60 degrees. Then, the other same-side interior angle must be 120 degrees, because 60 + 120 = 180. If they don’t add up to 180, then the lines are not parallel. Conversely, if they do add up to 180, congratulations, you’ve proven the lines are parallel!
Think of it as a seesaw. The transversal is the fulcrum, and the two same-side interior angles are on either side. To keep the seesaw balanced (i.e., the lines parallel), the angles need to add up to 180 degrees. Too much angle on one side, and the seesaw tips, meaning the lines are no longer parallel.