Geometry: Logic Statements

Introduction to Logic Statements

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.