Properties and parts of triangle

Introduction

Triangle is one of the most common shapes used in geometry. It is a polygon with three vertices and three sides which are called line segments. There are different types of triangles. All sides have the same length in an equilateral triangle. It is also a regular polygon and all its angles measure 60°. On the other hand, all sides are unequal in a scalene triangle. As a result all angles are also unequal. Right triangles are scalene. Two sides are of an equal length in an isosceles triangle. Two angles are also of the same measure.

Perpendicular bisectors

A perpendicular bisector of a triangle is defined as a line which passes through its midpoint to its side. As all triangles have three sides, all triangles have three perpendicular bisectors of their sides. All the three bisectors of sides of a triangle meet at a common point which is known as circumcentre. If the triangle is an acute triangle, then its circumcentre occurs inside the triangle. On the other hand, if the circumcentre of a triangle takes place outside the triangle, then the triangle is known as obtuse triangle. If the triangle is a right triangle, then its circumcentre will occur at the midpoint of the hypotenuse.

Angle bisectors

An angle bisector is a line which divides an angle into two equal parts. Within a triangle, there are three angle bisectors. They meet at a point which is known as in center of a triangle. When measured from a segment which is perpendicular to the sides of a triangle, an angle bisector is equidistant from sides of the angle.

Median & centroids

A median of a triangle is a line segment which joins the vertex to midpoint of the opposite side. There are three medians in a triangle, each passing through one vertex to opposite side. In equilateral and isosceles triangles, a median bisects any triangle whose adjoining sides are equal in length at a vertex. A median of triangle passes through its centroid i.e. the center of mass of object in uniform density in a triangle's shape. So, the object will balance on any line which passes through the centroid, including median.

Altitudes

Distance between a triangle's vertex and the opposite side is known as altitude. It is the length of the shortest line which passes between the vertex of a triangle and the opposite side. The orthocenter is the common point of the triangle through which its three common altitudes pass. In simple terms, altitude refers to height. It is the line at right angles to a side which goes through its opposite corner.

Conclusion

The midpoints and feet of three sides lie within a single circle and are called the triangle's nine point circle. The remaining three points are midpoints of the altitude which lies between the vertices and orthocenter. The nine point circle's radius is half of circumcircle It touches the three ex-circles and in-circle.

This article has been compiled by Evelyn, who is a writer on various academic topics.