A picture's worth a thousand words.
News flash: geometry is about more than simple little doodles. It's about huge complicated ones.
Lucky for you, those doodles are everywhere. From your spherical baby brother to your dad (who's a total square), shapes are how we make sense of the world around us. If that's the case, knowing how to spot 'em and show how they work could prove useful. At least that way, we'll be one step closer to avoiding a shapeless alien invasion.
Semester A is all about learning how to work with geometric tools from the undefined notions (how mysterious!) to a compass and straightedge. Then, logic and proofs will give us the tools we need to work with other figures (like…more points, lines, and planes). We'll discuss triangular congruence, similarity, and we'll even help them find their centers. By the time we're through with them, they'll be all SAS and no sass.
P.S. Geometry is a two-semester course. You're looking at Semester A, but you can check out Semester B here.
- Microsoft Office, Google Docs, or another word processing program
- A scanner (or access to one)
- A camera (a camera phone is sufficient)
- All other work can be done via the Shmoop website.
Knowledge of algebra concepts
Course BreakdownPurchase units individually
Unit 1. Intro to Geometry
We'll start off by introducing you to geometry and giving you a brief rundown of the reoccurring concepts you'll see throughout the course. We'll learn about some of its fundamental building blocks, like points, lines, and angles, and even venture into the third dimension and the Cartesian plane. Complimentary peanuts will be provided.
Unit 2. Reasoning and Proof
Ever wanted to be like the detectives or lawyers on Law & Order? If so, then this unit is for you. We'll learn everything about logic and reasoning, from conditionals and truth tables to syllogism and detachment. And of course, we can't forget the meat and potatoes of geometry: proofs. Pass the gravy, please.
Unit 3. Parallel and Perpendicular Lines
Soon after learning about the properties of parallel lines, we'll shake things up by throwing transversals into the mix. Make sure you hold onto your congruent angles, because these angles and their theorems are the main course of this unit. We'll perform constructions, prove theorems, and even talk about the slopes of these lines on the coordinate plane. And naturally, leaving out perpendicular lines just wouldn't be right.
Unit 4. Congruent Triangles
It's the same ol' same ol'. Well, we think that sameness—or congruence—can be good. (Oreos haven't changed in over 100 years and they're still delicious!) In this unit, we will learn how to prove congruence in triangles, and how to use that congruence to solve problems. We won't help you find a better place to stash your Oreos, though. You'll have to do that on your own.
Unit 5. Relationships Within Triangles
Up to now, most of our lessons have been focused on the tasty outer shell of triangles—properties that deal with their sides and angles, and proving congruencies. That's all good and fine, but the time has come for us to dive into the creamy center—special line segments and centers within the triangle, just dripping with delicious new postulates, corollaries, and theorems for us to enjoy.
Unit 6. Similarity
You probably thought you had escaped triangles, but we aren't finished with them yet. We're going to cover some new triangle theorems. At this point, these will practically seem like second nature. We'll also learn about the scale factor, which is the ratio by which the polygon is reduced or expanded. Who knew so much information was bundled up in just three sides?
- Course Length: 18 weeks
- Course Number: 310
- Grade Levels: 9, 10, 11
- Course Type: Basic
Algebra I—Semester A
Algebra I—Semester B
Just what the heck is a Shmoop Online Course?