FTCE Professional Education Practice Exam

Which property is true for an acute triangle?

1. It has one angle greater than 90 degrees

2. It has one angle that is exactly 90 degrees

3. All angles are less than 90 degrees

4. It has a right angle

The correct answer is: All angles are less than 90 degrees

An acute triangle is defined by the specific property that all of its internal angles are less than 90 degrees. This characteristic means that each angle contributes to the overall shape of the triangle, resulting in a sharp or pointy appearance, which is a direct reflection of the angles being acute. In geometry, the sum of the interior angles of any triangle is always 180 degrees. For an acute triangle, since each angle is less than 90 degrees, this restricts the angles to being between 0 and 90 degrees. This is fundamental to the classification of triangles based on angle measures. The other options refer to properties that describe different types of triangles. For example, having one angle greater than 90 degrees describes an obtuse triangle, while having an angle exactly 90 degrees describes a right triangle. Thus, since none of these characteristics apply to acute triangles, recognizing that all angles must be less than 90 degrees is essential for correctly identifying the properties of acute triangles.