To classify the triangle ABC, let's start by considering the given properties:
1. Angle Measures: The triangle has angles of [tex]\(60^\circ\)[/tex], [tex]\(60^\circ\)[/tex], and [tex]\(60^\circ\)[/tex]. Each angle is [tex]\(60^\circ\)[/tex], indicating that all angles in the triangle are equal.
2. Side Lengths: The triangle has three congruent (equal) sides.
Now, let’s go through the classification options:
### Types of Triangles by Side Length:
1. Equilateral Triangle: A triangle with all three sides of equal length.
2. Isosceles Triangle: A triangle with at least two sides of equal length.
3. Scalene Triangle: A triangle with all sides of different lengths.
Since ABC has three congruent sides, it is an Equilateral Triangle.
### Types of Triangles by Angle Measure:
1. Acute Triangle: A triangle where all three interior angles are less than [tex]\(90^\circ\)[/tex].
2. Obtuse Triangle: A triangle with one interior angle greater than [tex]\(90^\circ\)[/tex].
3. Right Triangle: A triangle with one interior angle equal to [tex]\(90^\circ\)[/tex].
Given that the angles of triangle ABC are [tex]\(60^\circ\)[/tex], [tex]\(60^\circ\)[/tex], and [tex]\(60^\circ\)[/tex], all angles are less than [tex]\(90^\circ\)[/tex]. Thus, it is an Acute Triangle.
Combining both classifications, the triangle ABC is an Equilateral Acute Triangle.
Therefore, the triangle ABC is correctly classified as:
Equilateral acute
So, the answer is:
- Equilateral acute
