Acute triangle
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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.
and 
is acute if and only if 
, 
and 
. This is known as the An equilateral triangle is always acute. In an acute triangle, the circumcenter, incenter, orthocenter, and centroid are all within the interior of the triangle.
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