The terminology for categorizing triangles is more than two thousand years old, having been defined on the first page of
Ancient Greek mathematician Euclid defined three types of triangle according to the … See more

Triangles are assumed to be two-dimensional plane figures, unless the context provides otherwise (see § Non-planar triangles, below). In rigorous treatments, a triangle is therefore called a 2-… See more

The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. That sum can equal the length of the third side only in the case of a degenerat… See more

There are thousands of different constructions that find a special point associated with (and often inside) a triangle, satisfying some unique property: see the article Encyclopedia of Triangle Centers for … See more

There are various standard methods for calculating the length of a side or the measure of an angle. Certain methods are suited to calculating values in a right-angled triangle; more complex methods may be required in … See more

The formulas in this section are true for all Euclidean triangles.
The medians and the sides are related by
and
,
and equival… See more

As discussed above, every triangle has a unique inscribed circle (incircle) that is interior to the triangle and tangent to all three sides.
Every triangle has a unique Steiner inellipse which is int… See more