They are a shape they are also both a polygon!
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An equilateral triangle is a triangle with three equal sides. An isosceles triangle is one with two equal sides. So yes, an equilateral triangle qualifies as being an isosceles triangle as well. This is quite similar to the relationship between squares and rectangles, where a square is always a rectangle, but a rectangle isn't necessarily a square.
Square, yes. Triangle, no.
A triangle can't be a square. A triangle only has 3 points, squares have 4.
If an equilateral triangle and a square have equal perimeters, then the ratio of the area of the triangle to the area of the square is 1:3.
A right angle triangle with 45, 45 and 90 degree angles is similar to an isosceles triangle