## 1.4 Theorems and Postulates

In this lesson I will introduce you to theorems and postulates. By the time you finish geometry you will have learned and studied many, many, many theorems and postulates. So, let me give you a quick definition on both of them- let's start with postulates first. A postulate is a mathematical law that we can't prove but we accept on faith. For example, the idea that two parallel lines never cross is a postulate- we accept this as fact but in mathematics we actually can't prove this. You maybe thinking that you can prove two parallel lines never intersect but if you put your arguments into a mathematical proof you would not be able to prove it. Just as a side note, famous mathematicians have tried to come up with a parallel line proof for hundreds and hundreds of years- so if you can prove it great! However just because we can't absolutely prove that parallel lines will never intersect we believe it anyway and turn our belief into a mathematical law. Now, that you have a sense of what a postulate is we can now define a theorem. A theorem is simply a mathematical property or law that we can prove using postulates and logic. Let's take a look at the lesson so you can start learning your first postulates and theorems in geometry.

__DIRECTIONS:__

- Watch The
**Lesson Video**First - Take Good Notes. - Next, Scroll All The Way Down The Page To View The
**Practice Problems**- Try Them On Your Own. - Check The Solutions To The Practice Problems By Looking At The Answer Key At The End Of The Worksheet.
- However,
**YOU MUST Still Watch The Video Solutions To The Practice Problems**; These Are The Videos Labeled EX A, EX B, etc. - They Are Located Next To The Lesson Video. - After You Do All Of The Practice Problems - Complete The Section and Advance To The Next Topic.

**Practice Problems:**