What Is Used to Support the Steps of a Geometric Proof?

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Several steps are involved in supporting a geometric proof, including obtaining or creating a statement of the theorem, stating the given, obtaining or creating a drawing that represents the given, stating what needs to be proved and proving the proof. Examples of geometric proofs include proving the areas of circles, triangles, parallelograms and trapezoids. Several proofs related to triangles exist, such as the angle sum, inequality and base angles theorems.

If the statement of what needs to be proved is not included with the problem, it may be researched or re-created by changing the information that is already given. The given is written as a geometric shorthand above or near the proof. It consists of the hypothesis and the facts required to prove the proof.

Drawing a picture not only illustrates the proof, but aids in plugging in values needed to prove it. The image drawn reflects what is being proved. The image should be large enough to easily view and include all labels such as A, B, C and D. Any additional mathematical facts such as congruency, should also be noted.

The statement of proof itself is written in geometric shorthand. Finally, the actual proof consists of a series of steps, each labeled, containing facts, postulates and theorems used to prove the statement.