Triangles are one of the fundamental figures used in Euclidean geometry. There are three elements required to make a triangle. It is a

• 3-sided
• plane or two-dimensional figure, in which
• the sum of the interior angles equals exactly 180 degrees.

There are two common systems of triangle classification. One focuses on the sides and designates three types of triangle.

Equilateral Triangle. Equilateral means “equal sides,” and in an equilateral triangle, all three sides are the same length. This means that the angles will also be equal – all 60° - making the triangle equiangular as well.

Isosceles Triangle. Isosceles means “equal legs,” and an isosceles triangle has two sides that are equal in length. This also means that the two angles formed where the equal sides meet the third side are equal.

Scalene Triangle. Scalene comes from a word meaning "uneven," and a scalene triangle has three unequal sides. As you might suspect, then, the three angles are unequal as well.

The other triangle classification schema approaches triangles from the point of view of the measurements of the internal angles. It, too, designates three types of triangle.

Acute Triangle. In an acute triangle, the largest internal angle is acute – less than 90°. This means that all the angles are acute.

Right Triangle. In a right triangle, there is one right angle – an angle of exactly 90°. This means that the other two angles will be acute.

Obtuse Triangle. In an obtuse triangle, one internal angle is obtuse. This means, again, that the other two angles will be acute.

Other Triangles. The word triangle is also used for things that bear some resemblance to a triangle, either in having the approximate shape of a triangle or in having three points that are connected in some way. The musical instrument called a triangle is a metal rod shaped like a triangle, except that one end is open. It is hung by a thin wire so that it can vibrate when struck by a triangle beater. It is used in both orchestral and band music. A so-called love triangle is a romantic situation that involves three people, and generally implies that they would each prefer a twosome.

Triangle is also used in reference to places that have a more-or-less triangular shape. The Bermuda Triangle, the area roughly marked out by Bermuda, Fort Lauderdale, and Puerto Rico, is a well-known bit of the planet because it has a reputation for unexplained disappearances. There are a number of Golden Triangles, including the area of Southeast Asia noted for its opium production, however, a golden triangle is also an isosceles triangle constructed so that the ration of the hypotenuse to the base is equal to the so-called golden ratio, so we come full circle back to mathematics.