Which kinds of figures are similar: hexagons, rectangles, or equilateral triangles?

Question

Which kinds of figures are similar: hexagons, rectangles, or equilateral triangles?

Answer 1

Figures are similar if they have the same shape - the size may be different.

All equilateral triangles have the same same shape (three equal sides, three equal angles). All equilateral triangles are similar.

A hexagon only needs to have six sides. Not all hexagons are the same shape. All hexagons are not similar.

A rectangle is a parallelogram with one right angle. The length and width can vary. Not all rectangles are the same shape. All rectangles are not similar.

Answer 2

(revised, because Mark M. has correctly understood the problem)
 
The definition of each 'kind' (or class) of object includes information about the angles and the sides of the member objects.
 
     object name          angles                                            sides                      similar?
     --------------         ----------------------         ---------------------------------              ----------
       hexagon

                 six, perhaps unequal

                  (but total to 720º)                six (perhaps unequal length)           no
 
     rectangle

               four equal, each 90º            four, two pairs of equal length           no
 
   equilateral triangle 

               three equal, each 60º            three, equal length                           YES