Geometric Proofs
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.
