If they do add up to exactly 180 though, then the lines are actually parallel. What Euclid is saying is that eventually, the lines are going to intersect somewhere, sometime. Let's also say that ∠ α and ∠ β add up to a number that's not 180°, the sum of two right angles.

Let's say we have two lines and another line that crosses both of them, like in the picture above. The original version of the parallel postulate goes something like this: if a straight line that crosses two straight lines makes two angles on the interior whose sum is less than the measure of two right angles, the two straight lines will intersect on the same side as those angles.Īre your eyes crossed yet? Because ours totally are.īasically, it all boils down to that transversal thing we were talking about earlier. It's like Geometry in Wonderland, and we'd suggest not going down that rabbit hole just yet. Mathematicians have even shown that there are weird types of 'non-Euclidean' geometry where the parallel postulate isn't true. It's not neat and simple like the others, and it can't really be proven. The fourth says that all right angles are equal. The first three talk about lines, line segments, and circles. And when they do, who you gonna call? Not Ghostbusters, that's for sure.Įuclid talked about five basic postulates. Remember when we talked about postulates a little while ago? Those bad boys will come back to haunt you. One of the many things Euclid did was start out with a bunch of basic postulates about the nature of geometry. A lot has happened in the last 2300 years.) Only with funnier jokes and more pop-culture references. So really, Euclid was the first to Shmoop geometry and we're just following in his footsteps. But he gathered up all the useful stuff that folks had been talking about for a while and presented it in a pretty comprehensible way. Well, not all of it, and he didn't exactly invent it. He practically invented geometry back around 300 BCE. It's sort of a miracle we haven't talked about him yet, since he's basically the father of modern geometry.

Cue thunderous applause and a few rogue tomatoes thrown by disgruntled geometry students. Let's all give a big thank you-yes, a thank you-to Euclid of Alexandria. We've covered a lot of geometric ground already, but we still haven't paid proper tribute to the guy who got us into this whole mess.

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