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No. An isosceles right triangle is a special case. There are many right triangles which are not isosceles.
Scalene triangles
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
Yes - in the case of triangles in Euclidian geometry. That is, basically triangles in a plane.
Nope sorry, a Rhombus will be split into 2 isosceles triangles and 1 equilateral triangle.