Triangles

A triangle is a polygon with 3 sides and 3 angles.

Since it is a polygon, it must be a closed, plane figure with straight line segments as its sides.

Triangles are named in two different ways:

• according to the types of angles they have
• according to the lengths of their sides.

Naming a triangle by the types of angles it contains:

You can think of it this way ---- every triangle has 2 acute angles. Find those 2 acute angles. Now find the third angle. That angle is the one that determines the name of the triangle. In each of the triangles below, 2 acute angles have been circled. Looking at the third angle (the one that is not circled) we can see that:

• in triangle 1, the third angle is acute, so triangle 1 is an acute triangle
• in triangle 2, the third angle is obtuse, so triangle 2 is an obtuse triangle
• in triangle 3, the third angle is a right angle, so triangle 3 is a right triangle

Naming a triangle by the length of its sides:

Triangles are also named based on their sides.

All of the sides of triangle 1 are all the same length. It is an equilateral triangle.

Two of the sides of triangle 2 are the same length. It is an isosceles triangle.

None of the sides of triangle 3 are the same length. It is a scalene triangle.