Geometry ConstructionsA series of free High School Geometry Video Lessons from Brightstorm.
Constructing the Circumcenter The point of concurrency of the three perpendicular bisectors of a triangle is the circumcenter. It is the center of the circle circumscribed about the triangle, making the circumcenter equidistant from the three vertices of the triangle. The circumcenter is not always within the triangle. In a coordinate plane, to find the circumcenter we first find the equation of two perpendicular bisectors of the sides and solve the system of equations.
Constructing the Orthocenter The orthocenter is the point of concurrency of the altitudes in a triangle. A point of concurrency is the intersection of 3 or more lines, rays, segments or planes. Theorthocenter is just one point of concurrency in a triangle. The others are the incenter, the circumcenter and the centroid.
Constructing the Centroid The centroid is the point of concurrency of the three medians in a triangle. It is the center of mass (center of gravity) and therefore is always located within the triangle. The centroid divides each median into a piece one-third the length of the median and two-thirds the length. To find the centroid, we find the midpoint of two sides in the coordinate plane and use the corresponding vertices to get equations.
Constructing a Perpendicular at a Point on a Line When constructing a perpendicular bisector, we are specifically being asked to construct a line perpendicular to a line through the midpoint. To construct a perpendicular to a line through a point like the midpoint, we use a process similar to constructing a perpendicular to a line through a point not on the line. To construct a perpendicular, we use a compass and straightedge to determine a point equidistant from two equidistant points on the line.
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