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Middle/High School Algebra, Geometry, and Statistics (AGS)
7.12 Theorem 22
Altitudes of a Triangle

An altitude of a triangle is a straight line through a vertex and perpendicular to (i.e. forming a right angle with) the opposite side or an extension of the opposite side.
The three altitudes of a triangle are concurrent, intersecting at the orthocenter.
The position of the orthocenter depends on the form of of the triangle:
  • Acute triangle the orthocenter lies within the triangle.
  • Right triangle the orthocenter lies on the hypotenuse of the triangle.
  • Obtuse triangle the orthocenter lies outside the triangle.