When we define and explain things in geometry, we use declarative sentences.
For example, "Perpendicular lines intersects at a 90 degree angle" is a
declarative sentence. It is also a sentence that can be classified in one, and
only one, of two ways: true or false. Most geometric sentences have this
special quality, and are known as statements. In the following lessons
we'll take a look at logic statements. Logic is the general study of systems of
conditional statements; in the following lessons we'll just study the most
basic forms of logic pertaining to geometry.
Conditional statements are combinations of two statements in an if-then
structure. For example, "If lines intersect at a 90 degree angle, then they are
perpendicular" is a conditional statement. The parts of a conditional statement
can be interchanged to make systematic changes to the meaning of the original
conditional statement. Based on the truth value (there are only two truth
values, either true or false) of a conditional statement, we can
deduce the truth
value of its
converse, contrapositive, and inverse. These three types of
conditional statements are all related to the original conditional statement in
a different way. By the end of this section we'll have a systematic way to use
definitions in geometric proofs.
The process of writing geometric proofs is very precise, and requires that we
define terms with exactness, and use those definitions appropriately. Here's a
look at logic statements.