How Acute Triangles Are Unique: Properties And Examples

acute triangle

a triangle where all three angles are < 90 degrees

An acute triangle is a triangle where all three interior angles are acute angles, which means they are less than 90 degrees. In other words, an acute triangle is a triangle whose three angles are acute (less than 90 degrees).

The term acute refers to the fact that the triangle’s angles are less than 90 degrees. It is the opposite of an obtuse triangle, which has one angle measuring greater than 90 degrees.

In an acute triangle, the sum of the three angles is always less than 180 degrees. Therefore, acute triangles are never considered as the right triangle or the obtuse triangle. Moreover, each side of an acute triangle is shorter than the hypotenuse of a right-angled triangle with the same base and height.

In geometry, acute triangles are important because they have some unique properties. For example, the intersection of the altitudes of an acute triangle is always inside the interior of the triangle, and so is the intersection of the angle bisectors. Additionally, the circumcenter (i.e. the center of the circumscribed circle) of an acute triangle is always inside the triangle, unlike the circumcenter of a right triangle or an obtuse triangle.

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