So whenever it was transposed the second chord was lowered a half-step or made flat.

I can almost hear you saying,...."but we didn't lower it a half-step in the first chapter"!

Oh yes you did! You just didn't know it! In the key of A, a 1-7-4 has the chord's A-G#-D, but I asked you not to worry about the sharps(#) and flat(b) characters because you needed the information in the chapter's on "Interval's" and "Sharp's and Flat's" before you could move forward.

That's something else that has to be remembered. If the arrangement you are using has a chord that does not match the scale for the key you are using, then the chord most likely has to be lowered or possibly raised a half-step in order to be transposed correctly.

Example; A# in the key of A, will transpose to G# in the key of G. Because the A is sharped the G must also be sharped.

A G note in the key of E would be a flatted note because the scale that must be followed shows a G#. If this note or chord has been flatted then the transposed note from the key of G to the key of F will be an Ab.