![]() While you often see these three types of triangles identified by the lengths of their sides, they can also be categorized by their angles. In our last triangle, none of the sides have the same length, so this is called a scalene triangle. It’s a hard one to spell, but an easy one to recognize! Scalene Triangle When two of the sides of a triangle are the same it’s called an isosceles triangle. In the middle triangle, we can see that two of the sides are the same length and measure 8 cm while the third is 9 cm. It’s not too tough of a name to remember since the beginning of equilateral sounds like the word equal, and the word lateral means “side.” Isosceles Triangle A triangle like this one where all the sides are the same is called an equilateral triangle. In the triangle on the left, we can see that all three sides are the same length and measure 9 centimeters. Here are three triangles with the lengths of the sides included: Our second set of triangles is categorized by how many of the sides have the same length. That’s all there is to it for these three types! We just find the largest angle and the name of the triangle will correspond to the name of that angle. ![]() Because this is more than 90 degrees, this is an obtuse angle, so we call this triangle an obtuse triangle. Obtuse Triangleįinally, in the triangle on the right, the largest angle is 117 degrees. ![]() You might remember that a 90-degree angle is a right angle, so this triangle is a right triangle. We can see that in the middle triangle the largest angle is exactly 90 degrees. This one is easy to remember, since “cute” things are often small, like puppies and kittens. Just remember that acute angles are less than 90 degrees. 70 is less than 90, so this is an acute triangle. We can see that the largest angle in the triangle on the left is 70 degrees. These are the acute, right, and obtuse triangles.īut how do you know which is which? Take a look at the largest angle of each triangle and note whether or not the angle is more than, less than, or equal to 90 degrees. Let’s start with the three types of triangles that are categorized by the measure of their largest angle. We’re going to break our six types of triangles into two groups of three. This is true for all triangles, including the six types we’re looking at today. In addition, a triangle has three interior angles, and the sum of those three angles is always 180 degrees. The length of the sides can vary but the length of the largest side can’t be equal or greater to the sum of the other two sides. Triangle E is an obtuse triangle since it has an obtuse angle, while triangle F is an acute triangle since all its angles are acute.Hi, and welcome to this review of different types of triangles! Before we begin, here’s a review of the basics.Ī triangle has three straight sides that connect. Furthermore, there can be at most one obtuse angle, and a right angle and an obtuse angle cannot occur in the same triangle. Proposition I.17 states that the sum of any two angles in a triangle is less than two right angles, therefore, no triangle can contain more than one right angle. Since triangle D has a right angle, it is a right triangle. An alternate characterization of isosceles triangles, namely that their base angles are equal, is demonstrated in propositions I.5 and I.6. It is only required that at least two sides be equal in order for a triangle to be isosceles.Įquilateral triangles are constructed in the very first proposition of the Elements, I.1. The way that the term isosceles triangle is used in the Elements does not exclude equilateral triangles. The term isosceles triangle is first used in proposition I.5 and later in Books II and IV. The equilateral triangle A not only has three bilateral symmetries, but also has 120°-rotational symmetries.Īccording to this definition, an equilateral triangle is not to be considered as an isosceles triangle. ![]() The scalene triangle C has no symmetries, but the isosceles triangle B has a bilateral symmetry. ![]() This definition classifies triangles by their symmetries, while definition 21 classifies them by the kinds of angles they contain. Further, of trilateral figures, a right-angled triangle is that which has a right angle, an obtuse-angled triangle that which has an obtuse angle, and an acute-angled triangle that which has its three angles acute. ![]()
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