The sum of the internal angles that exist at the vertices always total the same number for every triangle—180 degrees, or π radians.
In Euclidean geometry, any three non-collinear points determine a unique triangle and a unique plane.
Types of triangles
By relative lengths of sides
Triangles can be classified according to the relative lengths of their sides:
In an equilateral triangle, all sides are the same length. An equilateral triangle is also a regular polygon with all angles 60°.
In an isosceles triangle, at least two sides are equal in length. An isosceles triangle also has two equal angles: the angles opposite the two equal sides.
In a scalene triangle, all sides and internal angles are different from one another.
By internal angles
Triangles can also be classified according to their internal angles, measured here in degrees.
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A triangle that does not contain a right angle is called an oblique triangle. One that does is a right triangle.
There are two types of oblique triangles, those with all the internal angles smaller than 90°, and those with one angle larger than 90°.
The obtuse triangle contains the larger than 90° angle, known as an obtuse angle. The acute triangle is composed of three acute angles, the same as saying that all three of its angles are smaller than 90°.
A right triangle (or right-angled triangle) has one 90° internal angle (a right angle). The side opposite to the right angle is the hypotenuse; it is the longest side in the right triangle. Right triangles conform to the Pythagorean theorem: the sum of the squares of the two legs is equal to the square of the hypotenuse; i.e., a2 + b2 = c2, where a and b are the legs and c is the hypotenuse