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Formal Proofs, a la Shmoop.

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Dear Sir or Madam, you are cordially invited to attend the Formal Proof,

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a black tie event exclusively for geometers of the highest esteem.

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Upon arrival, please form two columns and show this invitation at the door for admittance.

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A-list members from all circles of the geometric world will be in attendance.

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So please wear your best surface area, and enjoy live music,

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complimentary cheesecake, and a night to remember.

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Proofs are all about showing evidence for why something is true,

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kind of like the detectives on your favorite crime show.

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Formal proofs take this a step further.

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They present the evidence in two columns:

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one for the statement they're claiming is true

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and the other for the reasoning behind them.

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Usually these reasons take the form of definitions, theorems, postulates, or given information.

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They lead us step-by-step from the hypothesis to the conclusion, like fancy tour guides.

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So if A equals B and B equals C, can we prove that A equals C using a formal proof?

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Well, let's give it a shot.

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First, we'll make two columns: tone for statements, one for reasons.

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We'll start with what we know.

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We can say that A equals B, because that's given to us.

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Same goes for B equalling C - given.

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We want to prove that A equals C,

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so we can use the transitive property of equality. That's all it takes.

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We've proved what we wanted to prove using a formal proof.

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Once you learn more definitions and theorems,

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you'll be able to write longer, more complicated proofs. Don't look too excited.

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If we can write formal proofs, we're certainly geometers of the highest esteem.

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So let's head to that ball and have ourselves a big old hunk of cheesecake…

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or five.

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