Orthocenter

Consider what happens with the position of the orthocenter when the triangle is right, obtuse, or equilateral.

Location for right triangles:
When the triangle is right, the orthocenter is the vertex of the triangle and the right angle. (Since this is where the two legs are altitudes.)

Location for obtuse triangles:
When the triangle is obtuse, the intersection of the altitudes is outside the triangle.

Location for equilateral triangles:
When the triangle is equilateral, the orthocenter is located at the same position as the centroid, circumcenter, and incenter.

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Click Here to use a GSP script for the construction of the orthocenter.

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Return to Write-Up 4 (Centers of a Triangle)

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Return to Write-Up 8 (Altitudes and Orthocenters)

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