5.2 Orthocenters of Triangles
The orthocenter of a triangle is a point of concurrency for the three altitudes of the triangle. In the triangle ABC below, each of the altitudes has been constructed. Remember, an altitude goes through a vertex of the triangle and is perpendicular to the opposite side. Modify the construction in order to examine the orthocenter of different types of triangles and explore the properties of the orthocenter.
Modify the shape of the triangle by dragging its vertices with the mouse. Change the measures of the angles, the lengths of the sides, and the location of the orthocenter. Move the vertices in multiple locations to observe changes when...
a) all angles are acute.
b) one angle is obtuse.
c) one angle is a right angle.
and then answer the questions below.
For what types of triangles is the orthocenter inside of the triangle?
For what types of triangles is the orthocenter outside of the triangle?
Where is the orthocenter for a right triangle?