Final answer:
An equilateral triangle is a special case of an isosceles triangle where all three sides and angles are equal. All equilateral triangles are also isosceles triangles, but not all isosceles triangles are equilateral triangles.
Step-by-step explanation:
An isosceles triangle is a triangle that has two sides of equal length and two equal angles opposite those sides. An equilateral triangle is a triangle that has all three sides of equal length and all three angles are equal to 60 degrees.
An equilateral triangle is a special case of an isosceles triangle where all three sides and angles are equal. Therefore, all equilateral triangles are also isosceles triangles, but not all isosceles triangles are equilateral triangles.
For example, in a regular icosahedron, which is a symmetrical solid shape with 20 faces, each face is an equilateral triangle. Therefore, each face is also an isosceles triangle.