Helpful Links
\(\bullet\) Interactive Triangle Orthocenter (geogebra.org)
\(\bullet\) Orthocenter Calculator (byjus.com)
Notes
Questions
Find the orthocenter of the following triangles with the following vertices.
\(\textbf{1)}\) \((1,2), (5,4), (3,4)\)
\(\textbf{2)}\) \((-8,0), (4,16), (12,10)\)
\(\textbf{3)}\) \((1,-2), (1,2), (0,3)\)
\(\textbf{4)}\) \((1,-2), (1,2), (3,0)\)
\(\textbf{5)}\) \((0,3), (2,2), (3,0)\)
\(\textbf{6)}\) \((-4,5), (0,1), (1,2)\)
\(\textbf{7)}\) \((-2,-1), (-2,7), (4,7)\)
See Related Pages\(\)
\(\bullet\text{ Geometry Homepage}\)
\(\,\,\,\,\,\,\,\,\text{All the Best Topics…}\)
\(\bullet\text{ Centroid}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Circumcenter}\)
\(\,\,\,\,\,\,\,\,\)
In Summary
The Orthocenter is a key concept in geometry that is used to describe the intersection of the three altitudes of a triangle. It is an important concept to understand because it allows us to make important measurements and calculations about triangles. The Orthocenter is defined as the intersection of the three altitudes of a triangle. An altitude is a line that is perpendicular to one of the sides of a triangle and passes through the opposite vertex.
Orthocenter is typically studied in a geometry class. It is typically learned during a chapter on triangles. The orthocenter is usually taught alongside the circumcenter, the incenter and the centroid.
Other points of concurrency in triangles
Circumcenter: The circumcenter of a triangle is the center of the circle that circumscribes the triangle. The Orthocenter and the circumcenter are often used together to calculate the radius of the circumcircle, which is the circle that circumscribes the triangle.
Incenter: The incenter of a triangle is the center of the circle that is inscribed in the triangle. The Orthocenter and the incenter are often used together to calculate the radius of the incircle, which is the circle that is inscribed in the triangle.
Centroid: The centroid of a triangle is the point where the three medians of the triangle intersect, and is often used as a reference point for analyzing the properties of the triangle.