# Higher Level Theorems

Euclid from The School of Athens by Raphael (1510-1511)

Steps in a Proof in Geometry.

1. Statement: State what you are going to prove.

2. Picture: Draw a suitable labelled diagram. Make it large enough to easily add all the detailed information. Be sure to label all the points with the appropriate letters. If lines are parallel, or if angles are congruent, include those markings, too.

3. Information: Say what you are given, (using the diagram and its labels).

4. Required to prove: Write down what you must prove.

5. Additions: (Possibly): Make any additions to the diagram that you will need. State clearly what you have done. (Some proofs do not need this step.)

6. Logical argument: Set out the steps of the proof. Give a brief reason for each statement you make.

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