Orthocenter of a Triangle
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Examples, solutions, videos, worksheets, games, and activities to help Geometry students learn how to construct the orthocenter of a triangle.
Orthocenter of a Triangle
The orthocenter of a triangle is one of the four classical triangle centers, along with the centroid, circumcenter, and incenter.
The orthocenter of a triangle is the point where the three altitudes of the triangle intersect.
The following diagrams show the orthocenters of different triangles: acute, right, and obtuse. Scroll down the page for more examples and solutions on the orthocenters of triangles.
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What is an Altitude of a Triangle
An altitude of a triangle is a line segment drawn from a vertex of the triangle perpendicular to the opposite side (or to the line containing the opposite side).
Every triangle has three altitudes, one from each vertex.
The altitude forms a right angle (90°) with the side it intersects.
How to Find the Orthocenter
To find the orthocenter of a triangle, you need to:
Draw (or construct) at least two of the three altitudes.
- From Vertex A, draw a line segment perpendicular to side BC (or its extension).
- From Vertex B, draw a line segment perpendicular to side AC (or its extension).
- (Optional) From Vertex C, draw a line segment perpendicular to side AB (or its extension).
The point where these two (or three) altitudes intersect is the orthocenter.
Location of the Orthocenter
The position of the orthocenter relative to the triangle depends on the type of triangle:
Acute Triangle: The orthocenter lies inside the triangle.
Right Triangle: The orthocenter lies exactly at the vertex of the right angle.
Obtuse Triangle: The orthocenter lies outside the triangle.
How to construct the Orthocenter of a Triangle?
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. The orthocenter is just one point of concurrency in a triangle. The others are the incenter, the circumcenter and the centroid.
This video demonstrates how to construct the orthocenter of a large scalene triangle using a compass and straightedge.
Constructing the orthocenter of a triangle
Using a straight edge and compass to create the external orthocenter of an obtuse triangle
Construct the Orthocenter of a Triangle
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