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Let ABC be a triangle. The triangle formed by the endpoints of the altitudes is called the orthic triangle of ABC.

The triangles cut off by the sides of the orthic triangle are similar to the original triangle.

See theorem 184 in N. Altshiller-Court, College Geometry, Mineola, NY: Dover, 2007 p. 97.

Contributed by: Jay Warendorff

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US Common Core State Standards, Mathematics

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The Triangles Cut Off by the Sides of the Orthic Triangle