CK-12 Geometry-Concepts

2.8. Two-Column Proofs http://www.ck12.org

2.8 Two-Column Proofs

Here you’ll learn how to write a two-column geometric proof.

What if you wanted to prove that two angles are congruent? After completing this Concept, you’ll be able to formally
prove geometric ideas with two-column proofs.

Watch This

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CK-12 Foundation: Chapter2TwoColumnProofsA

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James Sousa: Introduction to Proof Using Properties of Congruence

Guidance

Atwo-column proofis one common way to organize a proof in geometry. Two-column proofs always have two
columns- statements and reasons. The best way to understand two-column proofs is to read through examples.

When writing your own two-column proof, keep these things in mind:

• Number each step.


• Start with the given information.


• Statements with the same reason can be combined into one step. It is up to you.


• Draw a picture and mark it with the given information.


• You must have a reason for EVERY statement.


• The order of the statements in the proof is not always fixed, but make sure the order makes logical
  sense.


• Reasons will be definitions, postulates, properties and previously proven theorems.“Given” is only used
  as a reason if the information in the statement column was told in the problem.


• Use symbols and abbreviations for words within proofs.For example,∼=can be used in place of the word
  congruent. You could also use^6 for the word angle.