Flow Proof — Definition, Formula & Examples
A flow proof is a style of geometric proof that organizes statements in boxes connected by arrows, showing the logical flow from given information to the conclusion. Each box contains a statement, and the reason justifying that statement is written beneath or beside the box.
A flow proof (or flowchart proof) is a deductive argument presented as a directed diagram in which each node contains a proposition and its corresponding justification, and directed edges indicate the logical dependency between propositions, terminating at the statement to be proved.
How It Works
Start by placing each given statement in its own box at the top or left of your diagram. Draw an arrow from each box to the next statement it logically supports, writing the reason (postulate, theorem, or definition) below that new box. When two or more facts combine to justify a single conclusion, draw arrows from all of them into one box. Continue until you reach the final statement you want to prove. The finished diagram reads like a map of your reasoning, making it easy to see which facts depend on which.
Example
Problem: Given: ∠1 ≅ ∠3 and ∠2 ≅ ∠3. Prove: ∠1 ≅ ∠2.
Box A: Place the first given in a box: ∠1 ≅ ∠3. Write "Given" beneath it.
Box B: Place the second given in a separate box: ∠2 ≅ ∠3. Write "Given" beneath it.
Box C: Draw arrows from both Box A and Box B into a new box: ∠1 ≅ ∠2. Write "Transitive Property of Congruence" beneath it. Both earlier facts combine to support this conclusion.
Answer: The flow proof shows that ∠1 ≅ ∠2 follows from the two givens via the Transitive Property of Congruence.
Why It Matters
Flow proofs appear regularly in high-school Geometry courses as an alternative format on tests and homework. They are especially helpful when a proof has branching logic — two independent chains of reasoning that merge — because the diagram makes that structure visible in a way a two-column or paragraph proof cannot.
Common Mistakes
Mistake: Omitting the reason beneath each box, treating the flow proof as just a chain of statements.
Correction: Every box must have a justification (definition, postulate, theorem, or "Given") written directly below it, just as every row in a two-column proof needs a reason.