Types of Triangles by Length

In an equilateral triangle, all three sides are the same length. An equilateral triangle is always equiangular (see below).

In an isosceles triangle, two sides are the same length. An isosceles triangle may be right, obtuse, or acute (see below).

In a scalene triangle, none of the sides are the same length. A scalene triangle may be right, obtuse, or acute (see below).

Types of Triangle by Angle

In an equiangular triangle, all the angles are equal—each one measures 60 degrees. An equiangular triangle is a kind of acute triangle, and is always equilateral. 

In a right triangle, one of the angles is a right angle—an angle of 90 degrees. A right triangle may be isosceles or scalene. 

In an obtuse triangle, one angle is greater than a right angle—it is more than 90 degrees. An obtuse triangle may be isosceles or scalene. 

In an acute triangle, all angles are less than right angles—each one is less than 90 degrees. An acute triangle may be equilateral, isosceles, or scalene.