What is a quote that shows hamartia, one that shows peripeteia and one that shows anagnorisis in Macbeth?I'm doing an essay trying to prove Macbeth...

What a wonderful question! Here are examples of what you
are looking
for:

ANAGNORISIS

Let us begin
with a definition of anagnorisis. This Greek term, used by Aristotle, exemplifies a time
in a play where the protagonist comes to realize that something critical has happened. 
This tends to include awareness and realization of the moment and the impact it will
have in regard to other character's and the outcome for their life. An example of
anagnorisis in Macbeth:

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I'll go no more:/ I am afraid to think what I
have done;/ Look on 't again I dare not. (II, ii,
51-53)

What hands are here? ha! they pluck out mine eyes!/
Will all great Neptune’s ocean wash this blood/ Clean from my hand? No. (II, ii,
62-64).

HAMARTIA

Again,
developed by Aristotle (Poetics), hamartia is seen definable in many different ways.  It
can be looked at as a sin or wrongdoing.  It has also been defined in
Nicomachean Ethics (again by Aristotle) as being an injury one
person commits against another.

An example of hamartia in
Macbeth is:

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To know my deed, 'twere best not know myself
(II,ii, 78)

Here, Macbeth
acknowledges that the murder of Duncan's chamberlains was a wrongdoing.  He does not
even wish to look at who he really is because of how wrong he knows his actions
are.

PERIPETEIA

According to
Dictionary.com, peripeteia is "a sudden turn of events or an unexpected reversal,
especially in a literary work".  The sudden turn of events in Macbeth happens, again,
when Macbeth emerges from the chamberlains’ bedroom. He realizes what he has done is
wrong.  Macbeth, in he quest for the crown, realizes (only after he murders) that he is
wrong in committing the murder.  Unfortunately, Macbeth must revisit this later when he
questions the needed murder of Fleance and Banquo.  It seems that his first revelation
was not enough.