Triangle
A geometrical shape that has three angles is called triangle.
The name triangle splits into tri and angle. tri meaning three and angle is self explanatory. So, a shape with three angles is called triangle.
Terminology of a Triangle
We will introduce the terms used for a triangle, and these shall be used throughout our series of tutorials on Triangles.
Vertex
Vertex is the point where two sides meet.
In the above figure, vertices A, B and C are highlighted in blue.
Side
Side is the line segment joining two vertices.
In the above diagram, sides AB, BC and CA are highlighted.
Angle
The angle is the sweep formed between two sides at the vertex, inside of the triangle.
In the above diagram, the three angles are highlighted at the vertices of the triangle.
Altitude
Altitude is the perpendicular draw from vertex to the opposite side.
In the above figure, altitude is the perpendicular drawn from vertex C to opposite side AB.
You can also draw altitudes from A to BC and B to CA.
Angular Bisector
Angular Bisector is the line that passes through a vertex and bisects the angle at the vertex.
In the above figure, CP is the angular bisector at C.
Some of the terms are limited to specific type of triangles, and we shall discuss in detail at that juncture.
Different Types of Triangles
Categories based on equality in angles
Based on the equality in length of sides or equality in angles, triangles can be categorized into three categories. The three categories are provided in the following table, along with the information about their length of sides and angles.
| Category | Sides | Angles |
| Equilateral Triangle | Three sides are equal in length | All three angles are equal |
| Isosceles Triangle | Only two out of three sides are equal in length | Only two out of three angles are equal |
| Scalene Triangle | All three sides are unequal | All angles are unequal |
Categories based on type of angles
Also, based on the type of angles, triangles can be categorized into three. The three categories are given in the following table along with description.
| Category | Description |
| Acute Triangle | All the three angles are less than 90 degrees. |
| Right Triangle | One of the three angles is 90 degrees. |
| Obtuse Triangle | One of the three angles is greater than 90 degrees. |
Basic Properties of Triangle
What ever type of the triangle maybe, following basic properties apply.
Property 1: Sum of Angles
Sum of all three angles in a triangle is 180 degrees.
Property 2: Sum of Sides
Sum of any two sides is greater than the third side.
Property 3: Circumcircle
There exists a circle that touches all the three vertices of a triangle. This circle is called Circumcircle.
Property 4: Incircle
There exists a circle that touches all the three sides of a triangle. This circle is called Incircle.
Summary
In this Geometry tutorial, we learned about triangle, types of triangles, basic properties of a triangle.