He replied arrogantly.
They spoke arrogantly.
The opposite of the word arrogantly would be humbly.
There is no specific term for geeks acting arrogantly. Arrogant geeks is the word for them.
"We have finally captured you" the Major said arrogantly, while his Sargent-at-arms scowled fiercely at us.
arrogantly, proudly, loftily, boastfully
It's a verb (like walking proudly), and a noun (a building component), so depending on your context, something like "Johnny struts arrogantly around town, we all hate him" or "That building's struts aren't strong enough to support King Kong, someone get Faye Dunaway out of there".
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use contrast in sentence.