To show that you know something is to acknowledge it. Waving "hello" to acknowledge a friend and nodding your head "yes" to acknowledge that you agree with what's being said are both acts showing knowledge or acceptance of someone or something.

Dictionaries acknowledge that the word acknowledge has roots in the 15th and 16th centuries and is a combination of roots meaning "accord," "recognize," and "understand." Whereas "knowledge" is what you know, acknowledging is showing that you know. You might acknowledge that the world is round and that the moon is not made of cheese. You also can acknowledge, or give recognition, to the people who discovered these truths.

Definitions of acknowledge

v declare to be true or admit the existence or reality or truth of

“She acknowledged that she might have forgotten”
declare untrue; contradict
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acknowledge a new land owner as one's landlord
write off
concede the loss or worthlessness of something or somebody
make no bones about
acknowledge freely and openly
admit as valid
concede, confess, profess
admit (to a wrongdoing)
confess to God in the presence of a priest, as in the Catholic faith
confess, fink, squeal
confess to a punishable or reprehensible deed, usually under pressure
avouch, avow
admit openly and bluntly; make no bones about
fess up, make a clean breast of, own up
admit or acknowledge a wrongdoing or error
Type of:
adjudge, declare, hold
declare to be

v accept (someone) to be what is claimed or accept his power and authority

“The Crown Prince was acknowledged as the true heir to the throne”
know, recognise, recognize
Type of:
consider or hold as true

v accept as legally binding and valid

acknowledge the deed”
Type of:
consider or hold as true

v express recognition of the presence or existence of, or acquaintance with

“He never acknowledges his colleagues when they run into him in the hallway”
“She acknowledged his complement with a smile”
“it is important to acknowledge the work of others in one's own writing”
cite, mention
Type of:
react, respond
show a response or a reaction to something

v report the receipt of

“The program committee acknowledged the submission of the authors of the paper”
Type of:
communicate, pass, pass along, pass on, put across
transmit information

v express obligation, thanks, or gratitude for

“We must acknowledge the kindness she showed towards us”
recognise, recognize
recognize with gratitude; be grateful for
Type of:
give thanks, thank
express gratitude or show appreciation to

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