Triangles and regular polygons: Types and properties
In a nutshell
Triangles can be classified as rightangled, equilateral, isosceles or scalene, depending on their properties. All interior angles in a triangle add up to $\ {180 \degree}$. A regular polygon is a polygon with equal sides and equal interior angles.
Types of triangles
Triangle
 properties  Diagram 
Equilateral   Three equal sides.
 Three equal angles.
 Regular polygon.
 
Isosceles   Two equal sides.
 Two equal angles.
 
Scalene   No equal sides.
 No equal angles.
 
Rightangled

 Contains a rightangle.
 Triangles can be isosceles and rightangled.
 The side opposite the rightangle is the longest side (hypotenuse).
 
Regular polygons
A regular polygon is a polygon with equal sides and equal interior angles.
Regular polygon
 Interior angles  Number of sides  Diagram 
Equilateral triangle  $\ {60 \degree}$
 $\ {3}$
 
Square  $\ {90 \degree}$
 $\ {4}$
 
Pentagon  $\ {108 \degree}$
 $\ {5}$
 
Hexagon  $\ {120 \degree}$  $\ {6}$
 
Heptagon  $\ {128.6 \degree}$  $\ {7}$
 
Octagon  $\ {135 \degree}$  $\ {8}$
 
Example 1
Can you identify the type of triangle based on its properties described below?
 One right angle.
 Two equal interior angles.
 Two equal sides.
First, it can help to sketch the triangle.
Based on these properties, the shape is a rightangled isosceles triangle.
Example 2
Is a shape with eight equal sides and eight equal interior angles a regular polygon?
Yes, as all shapes with equal sides and equal interior angles are regular polygons.
This shape is an octagon.