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→Orthocenter of a Triangle
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−== Orthocenter of a Triangle ==
−
−From Greek: orthos -
−"straight, true, correct, regular" The point where the
−three altitudes of a triangle intersect. One of a triangle's points
−of concurrency.
−
−Try this Drag the
−orange dots on any vertex to reshape the triangle. Notice the
−location of the orthocenter.
−
−
−The altitude of a triangle (in the sense it used
−here) is a line which passes through a vertex of the triangle and is
−perpendicular to the opposite side. There are therefore three
−altitudes possible, one from each vertex. See Altitude definition.
−
−It turns out that all three altitudes always
−intersect at the same point - the so-called orthocenter of the
−triangle.
−
−The orthocenter is not always inside the triangle.
−If the triangle is obtuse, it will be outside. To make this happen
−the altitude lines have to be extended so they cross. Adjust the
−figure above and create a triangle where the orthocenter is outside
−the triangle. Follow each line and convince yourself that the three
−altitudes, when extended the right way, do in fact intersect at the
−orthocenter.
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−
* Direct substitution
* Direct substitution
−== Evaluation ==
== Evaluation ==