FTCE Professional Education Practice Exam

What is an obtuse triangle?

1. A triangle with all angles acute

2. A triangle with one obtuse angle

3. A triangle where all sides are different lengths

4. A triangle with only right angles

The correct answer is: A triangle with one obtuse angle

An obtuse triangle is defined specifically by its angles, and the key characteristic is that it has one angle that measures more than 90 degrees. This angle is known as an obtuse angle, making it distinct from other types of triangles. In an obtuse triangle, the presence of an obtuse angle dictates the overall shape and the relationships between the other two angles, which must each be acute (less than 90 degrees) to satisfy the triangle angle sum property, which states that the sum of all angles in any triangle must equal 180 degrees. The other options do not accurately describe the properties of an obtuse triangle. A triangle with all angles acute is referred to as an acute triangle, while a triangle with all sides of different lengths is known as a scalene triangle. Finally, a triangle with only right angles does not exist, as the sum of three right angles would exceed 180 degrees, thereby violating the foundational principles of geometry.