# What is a Triangle?

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

- Three-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.

**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 it *equiangular* as well.

**Isosceles Triangle.** *Isosceles* means “equal legs,” and this type 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 this type has three unequal sides. As you might suspect, then, the three angles are unequal as well.

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

**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 this type, there is one right angle — an angle of exactly 90°. This means that the other two angles will be acute.

**Obtuse Triangle.** This shape has one internal angle that 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 this shape, either in having the approximate form or in having three points that are connected in some way. The musical instrument called a triangle is a metal rod with three sides, except that one corner is open. It is hung by a thin wire so that it can vibrate when struck by a 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 ratio of the hypotenuse to the base is equal to the so-called *golden ratio*, so we come full circle back to mathematics.

## Discussion Comments

People may take a triangle for granted. But they can be very useful in building construction like Heartland said. So triangles are not just used in maths, but all around you. A very useful shape.

Triangles are often used in construction. They can be used as tools to ensure the project is square. They are also used in bridges to add strength and stability.

This is a good definition of a triangle in Euclidean geometry; however, it is noteworthy that there are other geometries in which a triangle may possess different properties. For instance, in spherical geometry, a triangle’s angles never add up to 180 degrees!

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