Question

A rectangle is sometimes, always, never similar to another rectangle

Answer 1

Two rectangles can be similar, but that's not always guaranteed.

In fact, similar shapes have the same angles and correspondant sides in proportion.

All rectangles will always have four right angles, so we only have to worry about the sides.

Let
`a,b` be the sides of a rectangle, with
`a\leq b`. Let
`c,d` be the sides of a rectangle, with
`c\leq d`.

Then, the two rectangles are similar if and only if

`a/ c=b/ d`

So, for examples, a rectangle with dimensions 3 and 7 is similar to a rectangle with sides 6 and 14 (both sides have been doubled), but it's not similar to a rectangle with sides 6 and 21 (one side has been doubled, the other has been tripled).