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Q: An equilateral triangle is always isosceles?

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Always

Yes.

An equilateral triangle is a special type of isosceles so an isosceles triangle can not be described as an equilateral triangle so, any equilateral triangle can be an isosceles triangle but an isosceles triangle can not be an equilateral triangle

An equilateral triangle is never an isosceles triangle. An equilateral triangle has three sides equal in length whereas an isosceles triangle only has two sides equal in length.

No, it is never the case.

sometimes, but not always

An isosceles triangle has at least two congruent sides. An equilateral triangle has three congruent sides. So, an equilateral triangle is a special case of isosceles triangles. Since the equilateral triangle has three congruent sides, it satisfies the conditions of isosceles triangle. So, equilateral triangles are always isosceles triangles. Source: www.icoachmath.com

No, none of the equilateral triangle will be isosceles.

Are isosceles triangle sometimes an equilateral triangle

If you can only prove two sides of an apparently equilateral triangle to be congruent then you have to use isosceles.

It can be scalene or isosceles but not equilateral.

The contrapositive would be: If it is not an isosceles triangle then it is not an equilateral triangle.

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