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Types of Triangles - Concept

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

Triangles can be classified by their angle measures and side lengths. For triangles only, equiangular and equilateral have the same implications: all sides and angles are congruent. Isosceles triangles have at least two congruent sides and two congruent angles. Right triangles contain an angle whose measure is 90 degrees. All the angles in an acute triangle are less than 90 degrees. Knowing the different types of triangles is important when solving proofs.

There are many different types of triangles and some of them actually overlap.
If we talk about an Equiangular triangle, we're talking about a triangle where the three angles are all congruent to each other and since the sum of these angles is 180, 180 divided by 3 means that each of these angles measures 60 degrees.
An equilateral triangle means that the three sides of your triangle are all congruent. Now just for triangles again this doesn't apply to quadrilaterals but just for triangles an equilateral triangle is the same as an equiangular triangle.
Moving on, if we have an isosceles triangle, which make sure you know how to spell this nothing drives Geometry teachers more insane than isosceles being spelt incorrectly, but an isosceles triangle has two sides that are congruent to each. So we're going to call these, legs and an isosceles triangle is not an equilateral triangle. But an equilateral triangle is isosceles, the reason is isosceles you only need two congruent sides which an equilateral triangle does have. For an equilateral triangle however, you need three congruent sides an isosceles doesn't have that many.
Next is a right-angle, excuse me a right triangle I got ahead of myself, a right triangle is identified by having one 90 degree angle. You can't have two 90 degree angles in a triangle because that will be a straight line and you couldn't form a triangle, so you know that in a right triangle your 90 degree angle will always always always be the largest angle.
Now comparing the three sides, we can identify scalene triangles. So let's say I told you that this was 6, 2 and 9 as the lengths of those three sides, that would be considered scalene because none of these sides are equal to each other. Just talking about the angles we can talk about acute triangles where all of these angles must be less than 90 degrees.
In an Obtuse triangle, one angle in which case it would be this angle right here, is more than 90 degrees so if it has one obtuse angle then the triangle is considered obtuse.
Well how come we use these distinctions to differentiate between triangles? Well, let's start by naming these four triangles. Here we have a 6, 7, 9 sided triangle, well I'm going to say that that is scalene, but if I look at this I have three acute angles and if I want to I could take my protractor and I can measure those three angles something that I did before I drew this up. So this is not only scalene but it is also acute so I can say that this triangle is a scalene acute triangle.
If I move on to this triangle right here, we can say that it is isosceles and again before I drew this up here I measured the angles with my protractor and they are all less than 90 degrees which means I could say this is an isosceles acute triangle.
So you can be more specific than just saying isosceles triangle, you could describe it as acute, obtuse or right which brings us to our next one where we have one obtuse angle, so this would be an isosceles obtuse triangle.
And last we have an isosceles triangle again because we have two congruent sides and a right angle so this will be an isosceles right triangle.
So you can use all of these terms together, not all but some, you can use obtuse and acute and right with isosceles and you can use acute and obtuse with scalene. So keep this training it could be very descriptive about how do you describe your triangles.

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