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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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