WHAT ARE THE ELEMENTS OF THE TRIANGLE? - CULTURE VOCABULARY - 2025

The elements of the triangle are divided into primary and secondary. They are the components that constitute it and define it as such. A triangle is a 3-sided polygon whose sum of its angles equals 180 degrees.

The primary elements correspond to the vertices, sides and angles, these can be interior or exterior.

The secondary ones refer to the height, orthocenter, bisector, incenter, bisector, circumcenter, and median. Normally in trigonometry time is only devoted to the study of the primary elements and additionally to the height.

Main elements of a triangle

When it comes to studying geometric figures, triangles play a key role, since they are considered the simplest polygons that exist as they have only 3 sides. Any polygon with 4 or more sides can be divided into a finite number of triangles.

Vertices

They are the points of origin of the triangle. Visually, a vertex can be defined as the place where the lines of a polygon are born and that define its limits.

They are easy to recognize as they dictate the overall size of the figure. They are usually denoted by the capital letters A, B, and C.

Sides

They are each of the lines that make up the triangle. One side is the space between 2 vertices defined with a straight line.

They are usually identified by the letters of the vertices at their ends, for example the side AB, or with the lowercase letters a, b and c, placing them on the opposite side of the vertices A, B and C.

The sum of the lengths of the sides of a triangle is known as the perimeter.

Angles

It is the degree of separation between 2 sides that start from the same vertex (interior angle) measured in degrees.

The sum of all the angles in a triangle is always 180 degrees. It is also possible to measure an external angle, in which case it is necessary to extend one of the sides.

Angles are identified by Greek letters such as alpha (α), beta (β), or gamma (γ).

Height

It is the measure of a perpendicular line (which forms an angle of 90 degrees), which goes from one vertex to the opposite side.

It is abbreviated as the letter h lowercase. A triangle can have 3 different heights, depending on the vertex that is being measured.

Orthocenter

When the 3 heights of a triangle are plotted, the point where the 3 lines touch is the orthocenter.

Bisector

It is a line that goes from one vertex to the center of the opposite side of the triangle, so it “divides” an angle in half. Depending on the type of triangle, the heights and bisectors can be the same.

Incenter

It is the point where the 3 bisectors meet.

Mediatrix

Also known as a symmetrical line, it is a perpendicular line to one side of a triangle that passes through its midpoint.

Circumcenter

It is the common point where the 3 mediatrices intersect. If a circle is drawn that touches the 3 vertices of a triangle, the circumcenter will be the center of the circle.

Median

It is a line connecting the midpoints of 2 sides.

References

1. What is a Vertex in Geometry (sf). Retrieved on November 30, 2017, from Study.
2. Elements of a triangle (sf). Retrieved on November 30, 2017, from CEIBAL.
3. Elements of the triangle (sf). Retrieved on November 30, 2017, from Online Professor.
4. The Secondary Elements of a Triangle (sf). Retrieved on November 30, 2017, from Uzinggo.
5. Carolina Pedroza (nd). Elements of the triangle. Retrieved on November 30, 2017, from Modern Mathematics.