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How to Do Geometry Proofs

Learning how to properly write geometry proofs can help you find out if a statement is true. Here's how to get started.


  • TIP: Write every step of the proof to make sure it is as detailed as possible, and don't skip a step.
  • Step 1: Prove the theorem by progressing through the statements until they conclude with your statement of theorem written at the bottom of the geometry proof.
  • FACT: The Greek philosopher Pythagoras, who is credited with writing the Pythagorean theorem, started a strict religious society in which the members had no possessions and were all vegetarians.
  • Step 2: List the statements and reasons to do your geometry proof. Make sure the statements progress in a sequential and logical way, with each statement building off the previous one.
  • Step 3: Write the theorem you are trying to prove at the bottom of the statements column. This will be your conclusion. Use geometric shorthand to write the statements.
  • Step 4: Split the page into 2 columns. Label the right column "statements," and the left column "reasons." Your proof should resemble the letter T.
  • Step 5: State the given in the statements column. In the reasons column, note that they are given.
  • Step 6: Draw a diagram, if one is not supplied, that contains all of the givens in the problem. Givens are the facts provided to help prove the theorem. Label the points and lines on the diagram, and detail what you are trying to prove.

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