Types of triangles

By internal angles

Triangles can also be classified according to their internal angles, measured here in degrees.

• A right triangle (or right-angled triangle, formerly called a rectangled triangle) has one of its interior angles measuring 90° (a right angle). The side opposite to the right angle is the hypotenuse; it is the longest side of the right triangle. The other two sides are called the legs or catheti[5] (singular: cathetus) of the triangle. Right triangles obey the Pythagorean theorem: the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse: a2 + b2 = c2, where a and b are the lengths of the legs and c is the length of the hypotenuse. Special right triangles are right triangles with additional properties that make calculations involving them easier. The most famous is the 3-4-5 right triangle, where 32 + 42 = 52. In this situation, 3, 4, and 5 are a Pythagorean Triple.

• Triangles that do not have an angle that measures 90° are called oblique triangles.

• A triangle that has all interior angles measuring less than 90° is an acute triangle or acute-angled triangle.

• A triangle that has one angle that measures more than 90° is an obtuse triangle or obtuse-angled triangle.

A triangle that has two angles with the same measure also has two sides with the same length, and therefore it is an isosceles triangle. It follows that in a triangle where all angles have the same measure, all three sides have the same length, and therefore such triangle is equilateral.

Right	Obtuse	Acute
	Oblique

By relative lengths of sides

Triangles can be classified according to the relative lengths of their sides:

• In an equilateral triangle all sides have the same length. An equilateral triangle is also a regular polygon with all angles measuring 60°.[1]
• In an isosceles triangle, two sides are equal in length.[2] An isosceles triangle also has two angles of the same measure; namely, the angles opposite to the two sides of the same length; this fact is the content of the Isosceles triangle theorem. Some mathematicians define an isosceles triangles to have only two equal sides, whereas others define that an isosceles triangle is one with at least two equal sides.[3] The latter definition would make all equilateral triangles isosceles triangles.
• In a scalene triangle, all sides are unequal.[4] The three angles are also all different in measure. Notice that a scalene triangle can be (but need not be) a right triangle.

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Equilateral	Isosceles	Scalene