# 1 – Foundations of Geometry

• Whenever Charlie’s home alone during a thunderstorm, he gets in trouble. So, if it’s thundering outside, and you know he’s by himself, you suspect the worst. You come in the front door and… Yep. It looks like Charlie struck again.
• You think you know what happened, but how can you prove it? Geometry can help. Yes, Geometry. It’s more than ancient Greeks and triangles.
• Geometry involves inductive and deductive reasoning. Inductive reasoning is a way of thinking that uses patterns from everyday observations to form a general rule. Deductive reasoning works in the opposite way – it starts with a general rule that you can then apply to everyday situations.
• Charlie’s past actions during thunderstorms helped you identify the general rule for how he’d behave. So, when you find Charlie surrounded by your destroyed furniture during a thunderstorm, you can safely deduce that he chewed it.
• Like a detective following clues, Geometry teaches you about logical thinking and investigating patterns. It identifies which things you can accept as givens, or postulates, and which things you need to prove.
• Geometry also introduces you to if-then statements. If you leave Charlie alone during a thunderstorm, then he will chew the furniture. Does it makes sense the other way around? If he chews my furniture, then you will leave him alone during a thunderstorm? No. Geometry studies which forms of if-then statements make sense.
• In this unit, you’ll get an introduction to Geometry and see the important role that logic will play in this course. You’ll learn to develop airtight arguments, and prove that you’re right.