Given any triangle, an altitude of
the triangle is the perpendicular line drawn from one of the vertices
to the opposite side.
The orthocenter of the triangle is
the point of concurrency of the altitudes.
Below is the triangle ABC with the
altitudes and the orthocenter constructed.
Notice, when we created the orthocenter
of triangle ABC, we divided the triangle into three more triangles
(DBC, DAB, and DAC).
If we find the altitudes and orthocenters
of the three smaller triangles, what happens?
The orthocenters of the three smaller
triangles are the vertices of the triangle ABC.
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