 So, by the way, with this particular proof, there's another way to go about proving it. And that proof, while that second way of proving it, does not use these vertical angles. And so all of this blue information we actually wouldn't use. And so instead of the blue angles at any w and p, e, t, we can still use the fact that n, w, and p, t are parallel, right, these segments. And that tells me that alternate interior angles are congruent. Well, angle w and angle t are also alternate interior angles. So we could use that information for the proof as well. The difference is, instead of using ASA, we would be using AAS. And here's why. In AAS, the side, the pair of sides I guess that are congruent are the non-included sides. And so if we just consider triangle n, e, w, if we just consider triangle n, e, w, we know that these segments are going to be used, or that segment I guess, this angle and this angle. Those are the used segments and the used angles in that proof. And you'll notice that the red segment is only connected to one of the angles. Right, it's only connected directly to that angle n. So we'll be using AAS. So let's do a little bit of rearranging of our proof. So since we're dealing with an angle-angle side proof, we'll have to talk about one pair of angles, which is shown here, another pair of angles, and then that pair of sides that we've already established. Okay, so from the fact that n, w is parallel to p, t, that gave us this first pair of angles that n and p were congruent. Now we also established that angle w was congruent to angle t. And the reason why is the exact same reason as n and p are congruent. It's the same pair of parallel lines but different transversal. And so the fact that n, w is parallel to p, t also gives us angle w and angle t congruent. And so that gives us our proof, which is similar to the previous proof, slightly different, it's using the AAS instead of the ASA. So I guess we've just established there's more than one way to prove this particular statement.