Not every isosceles triangle is equilateral. This is because they don't always have equal angles. The definition of an equilateral triangle is a triangle with all equal angles. However, every equilateral is an isosceles. This is because it would have at least 2 sides of equal length. The definition if an isosceles triangle is a triangle with at least two equal side lengths.
Every equilateral triangle is also anisosceles triangle, so any two sides that are equal have equal opposite angles. Therefore, since all three sides of an equilateral triangle are equal, all three angles are equal, too.
