Is there a term for two polygons with the same angles but different side lengths? Suppose polygons $A$ and $B$ have the same number of sides, and there is a correspondence between the vertices of $A$ and $B$, in consecutive order around both polygons, so that the angles at corresponding vertices are equal.  However, the lengths of the sides need not be equal.
For example:


*

*any two similar polygons are related in this way

*any two rectangles are related in this way

*these four hexagons share this relationship (modulo my drawing errors; all angles are supposed to be $90^\circ$ or $270^\circ$):



Is there a standard term for this relationship or property?
 A: "Angular congruence", perhaps?  I see it used occasionally, most clearly in http://www.gutenberg.ca/ebooks/dantzig-poincare/dantzig-poincare-00-h-dir/dantzig-poincare-00-h.html:

Thus, two rectangles may be dissimilar, although the corresponding angles are certainly congruent in this case; again, the sides of any rhombus are certainly proportional to the sides of any square, and yet the two figures are generally dissimilar. Angular congruence does by no means entail proportionality of lines.
The case of two similar triangles is an important exception. Here the congruence of corresponding angles does entail the proportionality of corresponding sides and, consequently, the similarity of the two figures. This property of similar triangles enabled Euclid to eliminate allusion to proportion and reduce the criteria of similarity of two polygons to congruence tests.

(Italics in original; bold face mine.)
A: I'd call such polygons (as those you depicted before your edit) parallel, and have heard them being called that way in personal conversations with other mathematicians, but I don't know whether this is in some way established. And it doesn't exactly fit if you only consider relative angles, i.e. if you rotate one of the figures as you did in your edit. You might want to call that a rotated parallel polygon, but that term sounds enough like a contradiction that I wouldn't use it without an accompanying definition.
I'm posting this as an answer, not a comment, so that people can express their (dis-)agreement using votes.
