acute triangle
a triangle where all three angles are < 90 degrees
An acute triangle is a triangle where all three angles are acute angles, which means that all three angles are less than 90 degrees. In other words, it is a triangle that has all angles less than a right angle.
Acute triangles have several unique properties. Here are a few key facts:
1. The sum of the interior angles of an acute triangle is always 180 degrees.
2. The altitude (height) from any vertex of an acute triangle always falls inside the triangle.
3. The circumcenter (the center of the circle passing through all three vertices) of an acute triangle is always inside the triangle.
4. The median (line segment connecting a vertex to the midpoint of the opposite side) from any vertex of an acute triangle always falls inside the triangle.
Acute triangles are important in many fields, including mathematics, engineering, and architecture. They are commonly used in trigonometry, where the ratios between the sides of acute triangles are used to solve problems involving angles and distances. Overall, understanding the properties of acute triangles is an important part of geometry and a foundational skill for many areas of study.
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