5 Questions
What is the defining characteristic of an acute triangle?
It has three acute angles
Why can't a Euclidean triangle have more than one obtuse angle?
It violates the sum of angles in a triangle
In an acute triangle, where are the orthocenter and circumcenter located?
Interior
What is the intersection point of the triangle's three altitudes called?
Orthocenter
What type of triangle does not have a 90° angle?
Oblique triangle
Study Notes
Properties of Triangles
- An acute triangle is defined by having all three angles acute (less than 90°).
- In a Euclidean triangle, it is impossible to have more than one obtuse angle (greater than 90°) due to the angle sum property of a triangle (180°).
- In an acute triangle, the orthocenter (the point where the three altitudes intersect) and circumcenter (the center of the circumscribed circle) are located within the triangle.
- The point where the three altitudes of a triangle intersect is called the orthocenter.
- Acute triangles are characterized by not having a 90° angle (right angle).
Test your knowledge of triangle types with this quiz! Identify acute and obtuse triangles based on their angle measurements. Learn about the defining characteristics of these two types of triangles.
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