Proof formats (two-column, paragraph, flow chart)
Proof Formats
Proof Formats is a topic in Proof & Reasoning in the Texas Essential Knowledge and Skills (Geometry, §111.41). It is aligned to Standard G.6, which requires students to construct proofs using two-column, paragraph, and flow-chart formats.
A geometric proof can be written as a two-column, paragraph, or flow-chart argument, each organizing statements and reasons deductively.
Theory
A proof is a logical argument from the Given information to the statement you must Prove. Every statement needs a reason — a given, definition, postulate, or proved theorem. Three formats present the same logic:
- Two-column — statements on the left, reasons on the right.
- Paragraph — the argument written in sentences.
- Flow chart — boxed statements linked by arrows showing the logic flow.
The structure of any proof:
How to write a proof
- List the Given and mark the diagram.
- State what you must Prove.
- Build a chain of statements, each with a reason.
- End with the statement to prove.
A proof starts with the Given information and ends with the statement to Prove.
The justification is the Vertical Angles Theorem.
| \(\angle 1\cong\angle 2\) | \(:\) | \(\text{Vertical Angles Theorem}\) |
Boxes joined by arrows form a flow-chart proof.
Every statement must have a reason — a given, definition, postulate, or previously proved theorem.
Common pitfalls
Frequently asked questions
What are the parts of a proof?
The Given information, the statement to Prove, and a sequence of statements each supported by a reason.
What is a two-column proof?
A proof with statements listed in the left column and the reason for each in the right column.
Does every statement in a proof need a reason?
Yes. Each statement must be justified by a given, definition, postulate, or proved theorem.
Are the proof formats interchangeable?
Yes. Two-column, paragraph, and flow-chart proofs present the same logical argument in different layouts.