To understand whether an equiangular triangle can ever be scalene, let's delve into the definitions and properties of both types of triangles.
1. Equiangular Triangle:
- An equiangular triangle is a triangle in which all three interior angles are equal.
- Since the sum of the angles in any triangle is always 180 degrees, each angle in an equiangular triangle must be 60 degrees (180 degrees divided by 3).
2. Scalene Triangle:
- A scalene triangle is a triangle in which all three sides and all three angles are different from one another. No sides or angles are equal in a scalene triangle.
Let's analyze the compatibility of these characteristics:
- An equiangular triangle has all equal angles (each 60 degrees), meaning it also has all equal sides. This type of triangle is also called an equilateral triangle.
- A scalene triangle requires all sides and all angles to be different, which directly contradicts having equal angles or sides.
Based on these definitions and characteristics, the properties of an equiangular triangle prevent it from being scalene. Hence, an equiangular triangle can never be scalene.
Therefore, the correct answer is:
A. True
An equiangular triangle can never be scalene.
