The goal of every geometry student is to be able to eventually put what he or she has learned to use by writing geometric proofs. Throughout the SparkNotes under Geometry 1 and 2 we have gained the knowledge to know what is and isn't true of a given geometric figure and why.

In this section, we'll develop the skills to show what we know in formal, two-column geometric proofs. Using deductive reasoning, geometric proofs systematically, lead a reader step-by-step from the premises of a proof to the conclusion--what may have been suspected (hypothesized), but wasn't known for sure. In the following lessons we'll study the form of a geometric proof, as well as different techniques for proving things geometrically.

The two major ways to prove a conclusion are by direct proof and by indirect proof. These two methods will be explained, along with the technique of drawing auxiliary lines. Auxiliary lines are lines that aren't given in the premises of a proof, but can be drawn (following the rules of geometry) to help demonstrate something about a figure or figures. Here we will put all of our knowledge to the test, not just by deducing things about a figure or figures, but by proving them systematically so that the whole world can understand what we've done.

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The Structure of a Proof