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Questions and Answers
What is the defining characteristic of an acute triangle?
What is the defining characteristic of an acute triangle?
- It has three obtuse angles
- It has three acute angles (correct)
- It has one obtuse angle
- It has one right angle
Why can't a Euclidean triangle have more than one obtuse angle?
Why can't a Euclidean triangle have more than one obtuse angle?
- It violates the sum of angles in a triangle (correct)
- It contradicts the law of sines
- It violates the Pythagorean theorem
- It contradicts Euclid's postulates
In an acute triangle, where are the orthocenter and circumcenter located?
In an acute triangle, where are the orthocenter and circumcenter located?
- Interior (correct)
- Exterior
- On the vertices
- On the midpoints of the sides
What is the intersection point of the triangle's three altitudes called?
What is the intersection point of the triangle's three altitudes called?
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What type of triangle does not have a 90° angle?
What type of triangle does not have a 90° angle?
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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).
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Description
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.
