FTCE Professional Education Practice Exam

What characterizes an acute triangle?

1. It has exactly one obtuse angle

2. It has exactly three acute angles

3. It has one right angle

4. It has no acute angles

The correct answer is: It has exactly three acute angles

An acute triangle is defined by its angles, specifically that all three angles are acute. An acute angle is an angle that measures less than 90 degrees. This characteristic is crucial because it means that the sum of all three angles in an acute triangle is always less than 270 degrees, but importantly, each individual angle must remain under 90 degrees. The defining feature of an acute triangle sets it apart from other types of triangles. For example, if there were an obtuse angle present, the triangle would be classified as an obtuse triangle instead. Similarly, a right triangle contains exactly one right angle, which is also a different classification. The option indicating that an acute triangle has no acute angles contradicts the very definition of what constitutes an acute triangle. Therefore, the characterization of having exactly three acute angles is what correctly defines this type of triangle.