Geometric Proofs Reference Sheet:
A geometric “proof” is a demonstration that a specific statement in geometry is
true. A sequence of true statements that include the given, definitions, or other
statements, that have been proved previously are linked by sound reasoning from one to
another until the desired conclusion is reached.
A proof consists of five parts: the diagram, the given statement, the prove
statement, the statements, and the reasons. We write a geometric proof in two columns;
the left column is for statements and the right column is for the reasons the statements are
true.
One of the most basic geometric proofs is that of congruent triangles, triangles
that are shown to be equal in size and shape. Showing that of the six parts of a triangle,
three sides and three angles, at least half of the corresponding parts of the two triangles
are equivalent often proves congruence.
When you write a proof, each statement should be dependent on the statement that
came before. Each reason should follow logically from the statement beside it, using the
key word in that statement. Mark corresponding parts of the diagram as you progress
through the proof.
Important Note:
Sometimes, instead of just being asked for a proof of congruence, you may be
required to prove other angles or line segments of the triangles congruent. That
automatically happens once the triangles are proved congruent, because:
C. P. C. T. C.
This abbreviation stands for “corresponding parts of congruent triangles are
congruent.” This can be used only after you have already proved that triangles are
congruent!!!