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Altitudes (heights) of a triangle

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An altitude (or the height) of a triangle is a line segment through a vertex and perpendicular to (forming a right angle with) a side of the triangle containing the base (the side opposite the vertex). This line containing the opposite side is called the extended base of the altitude. Every triangle has 3 altitudes which intersect at one point called the orthocenter (O).


In an acute triangle, all altitudes and the orthocenter lie within the triangle.

In a right triangle, two sides coincide with the altitudes and the orthocenter coincides with the vertex of the right angle.


In an obtuse triangle, two altitudes and the orthocenter lie outside of the triangle.



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