kolmnurka

Kolmnurka is a polygon with three sides and three vertices. It is the simplest closed shape that can enclose a region on the plane. In Euclidean geometry, the sum of its interior angles is always 180 degrees. A triangle can be examined by its side lengths, angles, or relations to other shapes.

Triangles are commonly classified by side lengths as equilateral (three equal sides), isosceles (two equal sides), and scalene (all sides different). By angles, they are acute (all angles under 90°), obtuse (one angle over 90°), or right-angled (one angle exactly 90°). The triangle inequality states that the sum of any two side lengths exceeds the third for every triangle to exist.

The area of a triangle can be found as base times height divided by two, or more generally as (1/2)ab sin C for sides a and b with included angle C. Heron's formula gives the area from all three side lengths: area = sqrt[s(s−a)(s−b)(s−c)], where s is the semiperimeter (a+b+c)/2. Pythagoras’ theorem applies to right triangles: a^2 + b^2 = c^2 for the legs a, b and hypotenuse c.

Key lines and centers associated with a triangle include the medians, which meet at the centroid; the angle bisectors, which meet at the incenter; and the perpendicular bisectors, which meet at the circumcenter. Every triangle has a circumscribed circle (circumcircle) and an inscribed circle (incircle).

Triangles are foundational in construction and design. They underpin trigonometry, enable area calculations, and form the basis of many geometric proofs and practical applications in surveying, computer graphics, and architecture.