The one thing that you often hear about when you hear the word 'geometry' is the word 'proof.' So, what IS a proof anyway, you might ask…a proof is an argument that utilizes logic, properties, previously-proven statements, definitions, and the like to prove that a conclusion is true. Think of it as an attorney arguing a case in court…!
When we justified our steps in Algebra, why, we were using proofs! Yep, that's right! Algebraic proofs use properties of equality as well as the Distributive Property to justify the reasoning used for each conclusion. The most critical component of a proof is that each step is not only shown but justified…and, we are not talking Justin Timberlake here! To justify each step, you can use a property, postulate, definition, or bit of given information.
When you solve an equation and you justify each step, then you are performing an algebraic proof. Let's see how a proof works in Algebra. Here's a typical problem: