FTCE Professional Education Practice Exam

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What defines a scalene triangle?

All sides are equal
Exactly two sides are equal
No sides are the same length
One angle is a right angle

The correct answer is: No sides are the same length

A scalene triangle is defined by the property that all three of its sides are of different lengths. This means that no sides are the same length, distinguishing it from other types of triangles, such as equilateral triangles (where all sides are equal) and isosceles triangles (where exactly two sides are equal). The identification of a scalene triangle is particularly significant in geometry as it highlights the variety in triangle classification based on side lengths. Options that refer to equal sides or specific angles, such as having two equal sides or possessing a right angle, do not describe the characteristics of a scalene triangle and instead pertain to isosceles or right triangles. Thus, the correct definition revolves around the uniqueness of each side length in a scalene triangle.