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Acute triangle

From AoPSWiki

An acute triangle is a triangle in which each angle is an acute angle. Any triangle which is not acute is either a right triangle or an obtuse triangle.

Acute triangles can also be defined in different ways:

  • A triangle is acute if and only if each of its altitudes lies entirely in the triangle's interior.
  • A triangle with sides of length and is acute if and only if , and . This is known as the Pythagorean Inequality.


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