Concept

Triangles are classified in the following ways:

Right--one right angle 
Acute--all acute angles 
Obtuse--one obtuse angle, and two acute angles 

Equilateral--equal sides and equal degrees
Isosceles--two sides are equal, and two congruent angles are equal
Scalene--no equal sides or angles

Rule

How to classify a triangle:

1. Compare the lengths of the sides.
   If the lengths are all the same, the triangle is equilateral.
   If only the lengths of the two sides are equal, the triangle is isosceles.
   If none of the sides are of equal length, the triangle is scalene.
2. Compare the angles.
   If one of the angles is 90 degrees, the triangle is right.
   If all the angles are less than 90 degrees, the triangle is acute.
   If one of the angles is more than 90 degrees, the triangle is obtuse.
   If two angles are congruent, the triangle is isosceles.

Example

The three sides of a triangle are 7 centimeters, 4 centimeters and 4 centimeters long respectively.

What kind of triangle is this?

Solution

Isosceles

1. Compare the lengths of the sides.
   The lengths are not all the same, so the triangle is not equilateral.
   The lengths of the two sides are equal (4 centimeters), so the triangle is isosceles.
2. No angles are given to compare.

Pre-requisite Skills

Measure Angles (4.10.1)