acute triangle
a triangle where all three angles are < 90 degrees
An acute triangle is a type of triangle where all of its angles are acute angles, meaning that they measure less than 90 degrees. Specifically, an acute triangle has three angles that each measure less than 90 degrees.
In an acute triangle, the measure of the longest side is shorter than the sum of the measures of the other two sides. This is known as the triangle inequality theorem, which states that for any triangle, the length of one side of the triangle must be less than the sum of the lengths of the other two sides, and greater than the difference of the lengths of the other two sides.
Acute triangles are commonly encountered in geometry and trigonometry, and they have many interesting properties. For example, the circumcenter, where the perpendicular bisectors of the triangle’s sides intersect, of an acute triangle lies inside the triangle, whereas for an obtuse triangle, the circumcenter lies outside the triangle. Additionally, the median, which is a line segment drawn from any vertex of the triangle to the midpoint of the opposite side, is always shorter than the corresponding altitude, which is a line segment drawn from any vertex perpendicular to the opposite side.
More Answers:
Acute Triangles: Definition And Application Of The Pythagorean Theorem.The Pythagorean Theorem For Right Triangles
Obtuse Angles In Math: Definition, Properties, And Real-World Examples