Wireless Security

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I have a family member who has a wireless dsl router at home. Right now it
is set up without encryption. She is out of state and I will be able to
set up the encryption function when I see her next, but that may be in a
while.
I have cautioned her that the connection is not secure as is and to use the
ethernet cable from the modem for safer communications. My primary
question is this. Is it "safe" (or reasonable so) to use secure web sites
for, let's say, ordering something on line, if the padlock icon is on? She
uses Internet Explorer.
Thanks
.