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Discovering Congruent Triangles through Transformations - So why are transformations important in Geometry? Well, transforming a shape is a great way to prove that one shape is congruent to another. When you don't change the shapes size, but instead map one shape to another perfectly, you can really see that they are congruent! Find out how to do that here!
Lesson - Discovering Congruent Triangles through Transformations
What you may need for this lesson: Graphing Coordinates on a Coordinate Plane PowerPoint
Supplementary, Complimentary, Vertical Angles, and Linear Pairs - Now that we know how to rigidly transform a shape, let's look at some specific angles and how they interact in geometry. This is essential for what we are going to cover later in the course. Check it out here!
Lesson - Supplementary, Complimentary, Vertical angles and Linear Pairs
What you may need for this lesson: Day 1 Construction
Corresponding and Vertical Angles - So we handled a bunch of angles before, but we're still not done naming the main angles that we are going to use, and geometry is very vocabulary based. Check out some of the remaining angles here!
Lesson - Corresponding and Vertical Angles
What you may need for this lesson: Day 1 Construction
Alternate Exterior & Alternate Interior Angles - Now that you've looked at some angles that are formed by parallel lines and a transversal, let's look at the last few that we need to go over!
Lesson - Alternate Exterior and Alternate Interior Angles
What you may need for this lesson: Day 1 Construction
Introduction to Proofs - So, why did we learn all of these angle names and characteristics? Well, because we're heading into proving mathematical arguments, and to do that, we need some knowledge. Proofs may be hard, but this lesson can help alleviate some of the pain! Found out how here!
Lesson - Introduction to Proofs
Proving Lines Parallel - Now that you have more experience under your belt when it comes to proofs, let's look at some common proofs that you can expect to see (as well as use) here!
Lesson - Proving Lines Parallel
Perpendicular Lines - Parallel lines are important, but they aren't the only lines that we are concerned with in geometry. Let's take a look at what perpendicular lines are and how they interact. Find out here!
Lesson - Perpendicular Lines
Slope and Parallel/Perpendicular Lines - So, seeing some parallel and perpendicular lines has helped understand how things work. But what about the equations that seem to work with parallel and perpendicular lines? Find out how the slope of a line can help you determine whether two lines are either parallel, or perpendicular.
Lesson - Slope and Parallel/Perpendicular Lines
What you may need for this lesson: The Many Faces of Slope PowerPoint
Triangle Sum Theorem - Now that we've covered most of the basic shapes that we can in geometry, let's talk a little bit about triangles. Mainly, how we know for a fact that no matter what kind of triangle you may find before you, all of the angles added together must equal 180 degrees. See how here!
Lesson - Triangle Sum Theorem
What you may need for this lesson: Undoing Procedures PowerPoint
Exterior Angles Theorem - You know that all triangles' angles add up to 180 degrees, but what happens if you have an angle that is attached to, but outside of, the original triangle? What does that mean? Find out here!
Lesson - Exterior Angles Theorem
What you may need for this lesson: Undoing Procedures PowerPoint
The Different Types of Triangles - So now, you know all sorts of interesting things about triangles. Their angle sum measure, the outside angle and its relation to the inside angles, and how they are formed. But that gets pretty tiring, and hard to work with at times, so to help lighten the load, here are some specific triangles that have properties that can help! Find out how here!
Lesson - Types of Triangles
What you may need for this lesson: Undoing Procedures PowerPoint
The Triangle Inequality Theorem - Now let's say you are trying to create a triangle, and you know two of the side lengths of this triangle, but you are not sure about the last one. Find out how to tell if three side lengths make a triangle or not!
Lesson - Triangle Inequality Theorem
What you may need for this lesson:
Proving Triangles Congruent with the Side Side Side Theorem - Here comes the big lesson in geometry, proving triangles are congruent. Why do we care? Because every shape you can think of can be broken down into triangles, and so if we know how to prove triangles congruent, we can prove anything congruent! But how do we prove triangles congruent? Well, there are a ton of ways, but this lesson will show you some very common ways to go about it. Check it out here!
Lesson - Proving Triangles Congruent With SSS
Proving Triangles Congruent with the Side Angle Side Theorem - We know how to prove triangles congruent with Side Side Side now, but is that the only way to prove congruence? Turns out, not so much! Turns out, if we have a side, an angle in between, and another side that is congruent to another side, angle, side, we also have congruent triangles! But how do we go about writing this proof? Well, there are a ton of ways, but this lesson will show you some very common ways to go about it. Check it out here!
Lesson - Proving Triangles Congruent With SAS
Proving Triangles Congruent with the Angle Side Angle Theorem - So, we've figure out side side side, side angle side, but can we do another one? Here is how to prove two triangles are congruent if you're down to just two angles, and the side in between them. Check it out here!
Lesson - Proving Triangles Congruent With ASA
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