Triangles have amazing properties! Among these is that the angle bisectors, segment perpendicular bisectors, medians and altitudes all meet with the rest of their kind. In this worksheet you can move around the vertices of a triangle and see how the different points move.
In a triangle, there are 4 points which are the intersections of 4 different
important lines in a triangle. They are the Incenter, Orthocenter, Centroid
and Circumcenter.
The Incenter is the point of concurrency of the angle
bisectors. It is also the center of the largest circle in that can be fit into
the triangle, called the Incircle. We say the Incircle is Inscribed in the
triangle.
The Orthocenter is the point of concurrency of the altitudes, or heights, as
they are commonly called. An altitude is the line perpendicular from a base
that passes through the opposite vertex.
The Centroid is the point of concurrency of the medians of a triangle. A
median is a line from a vertex to the midpoint of the opposite side.
The Circumcenter is the point of concurrency of the 3 segment
perpendicular bisectors of a triangle. The Circumcenter is the center of the circle
containing all three vertices, known as the Circumcircle. We say
that the Circumcircle is Circumscribed onto the triangle.
2014 - Albert Zhang