What is a Triangle?

The first and foremost thing that you must know about triangles is that they are polygons. As polygons, triangles present one of the basic shapes in geometry. Before we move on talking about types of triangles, it is very important that we understand what makes a triangle – triangle, meaning what are the rules for the existence of a triangle.

In order for a certain shape to be considered a triangle it must have three sides, and from these three sides, the length of two of the sides should be greater than or equal to the third side. So, the immediate question that pops on our heads is “what if the length of two sides is less than the length of the third side?” The answer is quite simple: “we will not have a triangle because in such cases any two sides of a triangle will never meet one another.”

With that being said, we also have to remember that the sum of the three angles within a triangle is equal to 180 degrees. So, let’s suppose we have a triangle and one of the angles within this triangle is equal to 130 degrees. Then, the sum of the two other angles must be equal to 50 degrees. If the sum of these two angles is less than or greater than 50 degrees, it means that we do not have a triangle.

Now that we understood what the rules for the existence of a triangle are, let’s check what are the types of triangles. There are two factors which determine the types of a triangle: the length of its sides and its interior angles. When considering the length of sides of a triangle, there are three types of triangles: an equilateral triangle, an isosceles triangle, and a scalene triangle.

A triangle is an equilateral triangle when the length of all its sides are equal. On such conditions (when all its sides are equal), also all its interior angles are equal – 60 degrees. A triangle is an isosceles triangle when the length of two of its sides are equal. On such conditions, the interior angles opposite to the two equal sides are also equal. A triangle is a scalene triangle when the length of none of its sides is equal. In a scalene triangle, also none of the angles is equal.

When looking at the interior angles, one of the triangles that comes immediately on our minds is the right triangle. In a right triangle, one of the interior angles is equal to 90 degrees, while the side opposite to the 90-degree-angle is called hypotenuse, which represents the longest side of the triangle. The other sides are called legs of the triangle. A special right triangle which you should keep in mind is an isosceles right triangle which has a 90-degree-angle and two equal interior angles (45 degrees). In this article, the specific rules, such as Pythagorean Theorem, which apply to right triangles is not covered, however it is very important that you know this basic information.

There are triangles which do not have any 90-degree angle, meaning that all of its angles are less than 90 degrees. These triangles fall under oblique triangles and are named Acute Triangles. There is another type of triangle that falls under oblique triangles, called Obtuse Triangle. Obtuse Triangles have an angle which is greater than 90 degrees, but the other two angles are less than 90 degrees.

We must understand that the topic of triangles is a very broad topic and requires books to cover everything related to triangles. However, with this article, we have tried to provide you the basic and most important information which will introduce you to triangles and some of their important features. Before we let you go, just another quick information: the sum of the three exterior angles of any triangle is 360 degrees.