An altitude of a triangle is a segment from any vertex perpendicular to the line containing the opposite side. The altitudes of a triangle are concurrent (they intersect in one common point). The point of concurrency of the altitudes is called the orthocenter of the triangle. (The prefix "ortho" means "right".) The altitudes' point of concurrency is not necessarily inside the triangle. It may actually be in the triangle, on the triangle, or outside of the triangle.
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In a right triangle, the altitudes intersect at the right angle.
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Locate the orthocenter through construction:
We have seen how to construct an altitude of a triangle. Simply construct the three altitudes of the triangle. The point where the altitudes intersect is the orthocenter.
Notice how it was necessary to extend the sides of the triangle for two of the constructions of a perpendicular from a vertex point to the opposite side.
The black point where the altitudes intersect is the orthocenter. |
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Actually, finding the intersection of only 2 altitudes will find the orthocenter. Finding the third altitude, however, will ensure more accuracy of the find. |
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