Question

Determine if the statement is always something or never true: Is a Scalene triangle a regular polygon?

A. Always true
B. Sometimes true
C. Never true
D. Depends on the angles

Answer 1

A Scalene triangle, which has sides and angles of different lengths, can never be a regular polygon because a regular polygon requires all sides and angles to be equal.

Step-by-step explanation:

The statement 'Is a Scalene triangle a regular polygon?' can be evaluated by understanding the definitions of a Scalene triangle and a regular polygon. A Scalene triangle is a type of triangle where all three sides are of different lengths, and consequently, all three angles are also different. By definition, a regular polygon is a polygon that is both equiangular (all angles are equal) and equilateral (all sides are of the same length). Since a Scalene triangle has sides and angles of different lengths and measures, it does not fit the criteria of a regular polygon.

Therefore, the correct answer to the question is C. Never true. A Scalene triangle can never be a regular polygon because its properties directly contradict the definition of regular polygons. Hence, regardless of the angles, a Scalene triangle will always have sides of different lengths, disqualifying it from being regular.