Classifying Triangles

Triangular Structure of Beryl Gem
Image Source:

The above diagram shows the atomic structure inside the crystal gemstone “Beryl”, which is composed of Silicon, Aluminium, Beryllium, and Oxygen ions.

Topaz, Olivine, Amethyst, and several other crystals found in nature also have triangular atomic structures.

The triangle is a natural shape which gives great strength to any structure.

Nature uses Triangles to make strong solid materials, which due to their internal geometry can be cut into beautiful gem stones.

Humans use Triangles to create strength in structures such as High Voltage Electricity Towers, structural frames for building and bridges, and even on farm gates.

worker and high voltage tower
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Types of Triangles

A triangle is a geometrical shape made up of 3 points called “Vertices” which are connected together by lines called “Segments”.

Eg. A triangle has three sides and is made of straight lines.

A triangle may be classified by how many of its sides are of equal length.

It can also be classified by what types of angles it has.

The vertices are labelled using upper case capital letters like A B and C, or D, E, and F, or P, Q, and R and so on.

The Angles inside the triangle which correspond to these Vertex points are labelled using lower case letters such as a,b,c or d,e,f and so on.

The line segments are labelled according to the vertex points that they connect to, such as AB, BC, or AC. Note that we keep the letters in alphabetical order, and also write lines above them to indicate that they refer to the linear sides of the triangle.

This is summarised in the following diagram.

Triangle Types - Classifying Triangles 1
Image Copyright 2012 by Passy’s World


There are four main types of Triangles that we use in the mathematics of geometry.

These are called “Equilateral”, “Isosceles”, “Scalene”, and “Right Angled” triangles.

The properties of these four types of triangles are shown in the following diagrams.

Triangle Types - Classifying Triangles
Image Copyright 2012 by Passy’s World

Triangles are also referred to as being either “Acute”, “Obtuse”, or “Right” Triangles.

“Acute” triangles have all three of their angles less than 90 degrees in size, such as the Equilateral and Isosceles triangles shown ablove.

“Obtuse” triangles contain one angle which is larger than 90 degrees, like the Scalene triangle shown above.

A “Right” Triangle that contains one L-shaped 90 degree angle is neither Acute or Obtuse. It is exactly inbetween these two, and is given the special name of “Right Triangle”.

This is summarised in the following diagram.

Classification of Triangles by Sides and Angles
Image Source:


Videos About Classifying Triangles

The following video explains how to classify triangles as Acute, Obtuse, or Right.


This next video is about Equilateral, Isosceles, and Scalene triangles.


Here is a great rocking music clip all about triangles.

Note that the word “Congruent” means “Identical” or “Equal”.


Classifying Triangles Worksheets

There are a number of different PDF worksheets, with answers available for free at the following links:


Classifying Triangles Games

Classifying Triangles Game 1

This first game involves getting Baseball hits everytime you classify a given triangle correctly.

Make sure you click on the right hand corner question mark to hear the instructions about how to swing at the ball.

Click the following link to play this fun game.


Classifying Triangles Game 2

In the above game we use the mouse to grab the triangles as they pass by, and place them into the correct basket.

Click the following link to play this game.


Classifying Triangles Game 3

This next game from BBC Mathematics is similar to the previous game, except that it focusses on Equilateral, Isosceles, and Scalene triangles, as well as some common four sided figures called “Quadrilaterals”.

Click the following link to play this game.


Related Items

Geometry Interactives at Geogebra
Interactives at Math Warehouse
Jobs that use Geometry


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