# for each file in the current directory you can refine the ls command to match
# only the files you want. or if in a script file pass in the file list
for file in *
do
# if the file has more than 10 lines.
if (( $(<"${file}" wc -l) > 10 )); then
# print line 3 to end of file and pipe it to a file with the same
# name as the input file with the added .checked at the end.
sed -n '3,$p' -- "${file}" > "${file}.checked"
fi
done