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A triangle having 3 congruent sides is an equilateral triangle
Triangles that have the same dimensions and the same 3 interior angles are said to be congruent to each other.
The 3 transformations of math are: translation, reflection and rotation. These are the well known ones. There is a fourth, dilation, in which the pre image is the same shape as the image, but the same size in the world
A triangle has 3 vertices, a rhombus has 4. All sides of a rhombus are of equal length, they need not be for a triangle. A triangle is a rigid shape, a rhombus is not.
The answer depends on whether the shape is 2-dimensional or 3-d. For a 2-dimensional polygon with n sides, the minimum number is n-3 diagonals.