Yes, all equilateral triangles are indeed acute and isosceles.
To understand why, let’s break down the definitions of these terms:
- Equilateral Triangle: An equilateral triangle is one where all three sides are of equal length. Consequently, all three angles in an equilateral triangle are also equal, each measuring 60 degrees.
- Acute Triangle: An acute triangle is defined as a triangle where all three angles are less than 90 degrees.
- Isosceles Triangle: An isosceles triangle is one that has at least two sides of equal length. In fact, all equilateral triangles fit this definition while having all three sides equal.
Since the angles of an equilateral triangle are 60 degrees, it satisfies the condition of being an acute triangle, as 60 < 90. Additionally, because it has all sides equal, it qualifies as an isosceles triangle as well. Thus, we can conclude that every equilateral triangle is both acute and isosceles.