![]() 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. ![]() The measures of the interior angles of the triangle always add up to 180 degrees (same color to point out they are equal).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. Elementary facts about triangles were presented by Euclid, in books 1–4 of his Elements, written around 300 BC. In rigorous treatments, a triangle is therefore called a 2- simplex (see also Polytope). Triangles are assumed to be two- dimensional plane figures, unless the context provides otherwise (see § Non-planar triangles, below). This article is about straight-sided triangles in Euclidean geometry, except where otherwise noted.Ī triangle with vertices A, īasic facts A triangle, showing exterior angle d. ![]() A curvilinear triangle is a shape with three curved sides, for instance a circular triangle with circular-arc sides. A geodesic triangle is a region of a general two-dimensional surface enclosed by three sides which are straight relative to the surface. In non-Euclidean geometries three straight segments also determine a triangle, for instance a spherical triangle or hyperbolic triangle. ![]() More generally, several points in Euclidean space of arbitrary dimension determine a simplex. In Euclidean geometry, any two points determine a unique line segment situated within a unique straight line, and any three points, when non- collinear, determine a unique triangle situated within a unique flat plane. Sometimes an arbitrary edge is chosen to be the base, in which case the opposite vertex is called the apex. The triangle's interior is a two-dimensional region. The corners, also called vertices, are zero- dimensional points while the sides connecting them, also called edges, are one-dimensional line segments. A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. ![]()
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