

Triangle
From Latin: tri "three" , angulus "corner, angle."
A closed figure consisting of three line segments linked endtoend.
A 3sided polygon.
Try this Drag the orange dots on each vertex
to reshape the triangle.
Triangle properties
Vertex 
The vertex (plural: vertices)
is a corner of the triangle. Every triangle has three vertices.

Base 
The base of a triangle can be any one of the three sides, usually the one drawn at the bottom.
You can pick any side you like to be the base.
Commonly used as a reference side for calculating the
area of the triangle.
In an isosceles triangle, the base is usually taken to be the unequal side.

Altitude 
The altitude of a triangle is the perpendicular from the base to the opposite vertex. (The base may need to be extended).
Since there are three possible bases, there are also three possible altitudes. The three altitudes intersect at a
single point, called the orthocenter of the triangle.
See Orthocenter of a Triangle.
In the figure above, you can see one possible base and its corresponding altitude displayed.

Median 
The median
of a triangle is a line from a vertex to the midpoint of the opposite side.
The three medians intersect at a single point, called the centroid of the triangle.
See Centroid of a Triangle

Area 
See area of the triangle and
Heron's formula

Perimeter 
The distance around the triangle. The sum of its sides. See Perimeter of a Triangle

Interior angles 
The three angles on the inside of the triangle at each vertex. See Interior angles of a triangle

Exterior angles 
The angle between a side of a triangle and the extension of an adjacent side.
See Exterior angles of a triangle

Also:
 The shortest side is always opposite the smallest interior angle
 The longest side is always opposite the largest interior angle
For more on this see Side / angle relationship in a triangle
Terminology
It is usual to name each vertex of a triangle with a single capital (uppercase) letter. The sides can be named with a single
small (lower case) letter, and named after the opposite angle.
So in the figure on the right, you can see that side b is opposite vertex B, side c is opposite vertex C and so on.
Alternatively, the side of a triangle can be thought of as a
line segment joining two vertices. So then side b would be called
AC.
This is the form used on this site because it is consistent across all shapes, not just triangles.
Properties of all triangles
These are some well known properties of all triangles. See the section below for a complete list
Types of Triangle
There are seven types of triangle, listed below. Note that a given triangle
can be more than one type at the same time.
For example, a scalene triangle (no sides the same length) can have one interior angle 90°, making it also a right triangle.
This would be called a "right scalene triangle".
Classifying triangles
The seven types of triangle can be classified two ways: by sides and by interior angles.
For more on this see Classifying triangles.
Constructing triangles
Many types of triangle can be constructed using a a compass and straightedge using the traditional
Euclidean construction methods.
For more on this see Constructions using Compass and straightedge.
Other triangle topics
General
Perimeter / Area
Triangle types
Triangle centers
Congruence and Similarity
Solving triangles
Triangle quizzes and exercises
(C) 2011 Copyright Math Open Reference. All rights reserved

