The terms acute, right and obtuse refer to the maximum angle measurement within a triangle. A right triangle contains a 90 degree angle. Because triangles consist of three angles totaling 180 degrees, both remaining angles within a right triangle must be less than 90 degrees.
Obtuse refers to triangles containing an angle greater than 90 degrees. Like right triangles, the remaining angles in an obtuse triangle must both measure less than 90 degrees. Acute triangles are triangles where none of the interior angles measures 90 degrees or greater.
The terms acute, right and obtuse can be used to further classify triangles within trigonometry; for example, a "right isosceles triangle."
The term "isosceles" is derived from the Greek terms iso and skelos, literally translated as "same legs." An isosceles triangle consists of at least two sides of the same length, although all three sides may be the same, and two angles of the same measurement.
An isosceles right triangle must contain a 90 degree angle. Because an isosceles triangle contains two angles of the same measurement, this means the remaining two angles within an isosceles right triangle must be 45 degrees.
Equilateral triangles are isosceles triangles whose sides all measure the same length. An equilateral triangle also contains three like angles. Because the sum of the three angles within a triangle must equal 180 degrees and all angles are equal, equilateral triangles always consist of three 60 degree angles, regardless of the length of the legs. Equilateral triangles are symmetrical when divided straight through the center of any interior angle.
Scalene triangles have no like measurements among the legs and angles. Scalene triangles may be right, acute or obtuse triangles, depending on the measurement of the angles inside the triangle. Because no two sides measure the same length, scalene triangles are always asymmetrical.