Triangle Classifications

In mathematics, triangle classification is the classification of triangles into categories based on their properties. The triangle classification problem was first posed by Hilbert in 1902 and solved in the negative in 1983 by Robertson and Seymour. Classification of triangles is an important problem in computer vision and image processing, and is used for example in image analysis and automatic optical inspection.

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Video Transcript

Hey, guys. Mr. Kleinberg Here, Um, we're here to talk about triangles, which is basically your most basic form of a polygon. But before we talk about triangles in general, let's talk about polygons. Okay, so you've all probably heard of the word polygon before, and a lot of us think that probably gone means multi angle when really it means multi side. Polly means many gone means side. I believe in Latin, so there's a many sided. Here's some examples. Okay, These are examples of polygons, so non examples would be like a circle or open figure or a figure that crosses itself. What a polygon has to be is a plainer which means two dimensional figure whose sides are made up of Lyon segments and has to be closed unlike the figure here, and it can't overlap itself. Unlike the figure here, now we can call a triangle a try gone meaning three sides. But oftentimes, for whatever reason, we call try Gon's triangles and it's been that way for forever. So if we talk about triangles, there are two major ways to classify them. Bye the sides of a triangle and by the angle measure. So there are three possible side classifications, so you can have what we call a scaling triangle in which there are no sides of equal length. That's what a scaling triangle is. You can have an isosceles triangle in which exactly two sides are equal length. Pardon me. We use those two little tick marks or dashes. Thio indicate equal length. We can also have what we call an equal lateral triangle. That's this one right here. Equi, lateral, equal money, equal lateral meaning side who think like a lateral toss and football it's tossed to the side. Those are your three types of of angle or sorry side classifications when it comes to triangles. But in terms of angles, you can also have these types of triangles. Okay, this has one of two single. This isn't up to strangle. It has an angle. One angle that's greater then 90 degrees. That's what makes it so your angle theta we call fate. It's like X. Your angle is greater than 90 degrees, or you can have a right triangle in which you have a 90 degree angle. Or you can have what we call an acute triangle. A C u T E we're all angles are less than 90 degrees. So these are your different types of classifications, by side or by angle. So if we take a look at this work sheep and it says, classify each triangle by angle inside, let me scroll down here. Actually, where I have measure, you can see that this first triangle has all equal sides all equal angles. This is definitely classified is an equal lateral if you want to classified by sides. Okay, bye angle. It would be an acute because all of the angles are less than 90 degrees. If you look at option eight, all the side links are different. So if we're talking about sides, we're gonna call it scaling also all three angles or less than 90 so we can call this acute. So if you look at nine, it's got a right angle. This is a right stealing triangle because no sides are equal. Question 10, you can see the two sides are equal, so we're gonna call this isosceles, and it looks like we have an obtuse angle and angle greater than 90 someone called also to use based upon its ankle measure and so forth. Look at 12 12 is because we have equal sides. It's Isis Elise, but it's got a 92 your angle, so it's a right triangle. So that's how we can classify triangles by the sides and by their ankles. And if you look, we'll do a couple more examples. You look at 14 14. Clearly should be ice oscillates because we have to equal sites. This would be a right angle because we know it's got all right angle by the marking. If we had a protractor and we could actually measure the angles that we can actually determine whether or not we have a cute or writer obtuse questions 18 is going to be a sausage because two sides are equal in a right angle. So it's a right triangle is well, so these are just a couple of examples of how to classify triangles. Um, they're a subset of polygons. We'll talk about other sided polygons like kwacha, laterals later but triangles or your most basic. And soon we'll start getting into the properties of different types of triangles and talking about how can we improve triangles, congruent, meaning, How can you? How can you prove that one triangle is the same size or shape as another triangle, or at least proportional to another triangle, as we would call them. Similar. So more on that later. I'll see you soon.