Given a triangle with side lengths $10$ in., $10$ in., and $10$ in., which classification best represents this triangle?

• A. Right triangle
• B. Scalene triangle
• C. Equilateral triangle
• D. Isosceles triangle

Answer: (C)

Verified step by step guidance

1. Step 1: Identify the given side lengths of the triangle. Here, all three sides are 10 inches each.
2. Step 2: Recall the definitions of triangle classifications based on side lengths: an equilateral triangle has all three sides equal, an isosceles triangle has exactly two sides equal, and a scalene triangle has all sides of different lengths.
3. Step 3: Compare the given side lengths to these definitions. Since all three sides are equal (10 in., 10 in., 10 in.), the triangle fits the definition of an equilateral triangle.
4. Step 4: Understand that an equilateral triangle is also equiangular, meaning all its interior angles are equal, each measuring 60 degrees.
5. Step 5: Conclude that the best classification for this triangle, based on the side lengths, is an equilateral triangle.