How many times have you heard one of your parents ask, "Who ate all the ice cream?" When no one admits to being the culprit, they may point a finger at you and accuse you of taking the last helping. How did they arrive at such an accusation? They made a conjecture, a reasonable guess based on observation that may or may not be true. After all, they reasoned, ice cream is one of your favorite foods, and there was some left when your parents went to bed last night while you stayed up to watch that late movie.
Conjecture is used to form a starting point when making an argument. As you can see from our ice cream example, you make conjectures every day in many ways. In fact, our entire judicial system revolves around the use of conjecture. Innocent until proved guilty is the foundation of our justice system, and conjecture is the means by which we arrive at our conclusion or verdict. Our judicial system relies on evidence and proof in order to hand out justice. Each accused person has a fair trial, and there must be enough proof in order to find them guilty of a crime.
Math is a lot like our judicial system. We can't just say something is true—we need to prove it. In the study of geometry, we use theorems and properties that have already been proven to help us do that. In this lesson, we're going to put them together to complete some proofs.
Before we begin, let's stop to think about proofs.
Question
Can you remember what an informal proof is?
An informal proof is one that is written in a way that does not explicitly state the rules used in each step. An informal proof can be written in many forms, including a list or a paragraph.
