Explain: every equilateral triangle is isosceles, but not every isosceles triangle is equilateral

By definition an isosceles triangle has AT LEAST 2 equal sides and AT LEAST 2 equal angles.  In an equilateral triangle, all 3 sides and angles are equal.  Since 3 is at least 2, an equilateral triangle is also an isosceles triangle.  An isosceles triangle does not have to have 3 equal sides and angles (which is equilateral), so that means an isosceles triangle may not be equilateral.