Ham op wrote:

A balanced antenna fed with balanced line, and the line goes away from
the antenna perpendicular [90 degrees angle] for a minimum of 1/4
wavelength is a properly installed antenna system: [line has minimum or
no radiation]

The line will have minimum or no radiation only if fed at the
transmitter end with a balanced feed. An unbalanced feed will create
unequal currents in the conductors, resulting in radiation. A
symmetrical (e.g., twinlead) line doesn't assure balance (equal and
opposite currents in the two conductors), and an unbalanced line will
radiate, regardless of its physical construction.

A balanced antenna fed with balanced line, and the line goes away from
the antenna non-perpendicular [other than 90 degrees angle] for a
minimum of 1/4 wavelength is an improperly installed antenna system:
[line will radiate]

True for both symmetrical line and coax. Radiation is due to common mode
current induced on the line. It can be reduced by inserting "current
baluns" (common mode chokes) in the line. A couple spaced about a
quarter wavelength apart are usually adequate.

A balanced antenna fed with un-balanced line, and the line goes away
from the antenna perpendicular [90 degrees angle] for a minimum of 1/4
wavelength is an improperly installed antenna system: [line will radiate]

The amount of common mode current and therefore radiation depends on the
length of the path along the outside of the coax to ground. A current
balun (common mode choke) at the feedpoint will reduce the current and
therefore radiation.

A balanced antenna fed with un-balanced line, and the line goes away
from the antenna non-perpendicular [other than 90 degrees angle] for a
minimum of 1/4 wavelength is an improperly installed antenna system:
[line will radiate]

This is due to induced common mode current. The mechanism is identical
to that when a symmetrical line is used.

A balanced antenna fed with un-balanced line and a properly installed
balun, and the line goes away from the antenna perpendicular [90 degrees
angle] for a minimum of 1/4 wavelength is a properly installed antenna
system: [line has minimum or no radiation].

Correct. A current balun at the feedpoint reduces the conducted common
mode current. Induced common mode current is prevented by symmetrical
feedline placement.

An un-balanced antenna fed with balanced line is an improperly installed
antenna and the line will radiate.

Coax feeding an unbalanced antenna will radiate just as much as twinlead
feeding an unbalanced antenna.

NEED I CONTINUE??

A lot of people have learned a list of handy rules like this without
having much of an understanding of where they came from or under what
circumstances they do and don't apply. For anyone interested in learning
more about common mode current, feedline radiation, types of feedlines,
and feedline radiation, I suggest taking a look at
http://eznec.com/Amateur/Articles/Baluns.pdf. It deals only with
conducted common mode current and doesn't discuss induced common mode
current -- I'll try to get together a supplement covering that topic
when I have time. There was some discussion on this newsgroup not long
ago about induced common mode current, but I can't locate the topic
right off. It should be possible to find it with a google search. Be
sure to also look at the work by Walt Maxwell, W2DU referenced at the
end of the balun article.

Roy Lewallen, W7EL