Are you taking geometry? Or do you just want to learn all about cool shapes? You've come to the right place! Rectangles, triangles, circles, pyramids, prisms, you name it! We're gonna talk about it.

What's a median? Or an altitude? They are special lines you can make with a triangle. And what's a circumcenter, or a centroid, or an orthocenter? These are some special points that relate to triangles. Not every geometry course covers this terminology, but it's super interesting, so take a look!

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OVERSEAS

Special Lines in Triangles: Bisectors, Medians, and Altitudes

We introduced a number of three-dimensional shapes in the last clip, but we still just talked about two-dimensional surface area. What's up with that? Alright, alright, let's learn how to calculate the three-dimensional volume that a shape will occupy. This is like the amount of water that a shape could hold if it was perfectly hollow. This can be a little tricky for the more complicated shapes, but there are equations we can memorize if we so desire. Check it out!

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Three-Dimensional Shapes Part 2: Calculating Volume

You may have heard the term perimeter before, in like a spy movie or something. What does it mean in geometry? Find out here!

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Calculating the Perimeter of Polygons

Pythagoras wasn't the only Greek fellow that was into math, you know. A little bit later, a fellow named Euclid built upon the work of old Pythag, and turned geometry more or less into what we learn in school today. Pretty impressive stuff! Let's learn some basic terminology so that we can maneuver this mathematical wonderland.

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Basic Euclidean Geometry: Points, Lines, and Planes

Is there anything more aesthetically pleasing than a perfect circle? It may seem like the king of shapes, but it's also arguably the simplest. Define a central point and a radius, and you've got a circle. What else can we say about circles? Let's find out!

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Circles: Radius, Diameter, Chords, Circumference, and Sectors

We learned about the Pythagorean Theorem, but where did it come from? How do we know it's definitely true? What if old Pythag just made it up off the top of his mystical skull? Lucky for us, in math we can proof that things are definitely true, and there are tons of ways to prove that the Pythagorean theorem is true. Here's one of the simpler ones for you to memorize, so you can bust it out at a party and be the coolest kid in the room!

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Proving the Pythagorean Theorem

We know about all kinds of one-dimensional parameters, like side lengths and what not, but now we want to talk about the two-dimensional area that a shape will occupy. This can be thought of as the amount of surface that a shape covers. In this clip, we go over some of the formulas we can use to calculate the area for different shapes, and how these are derived.

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Calculating the Area of Shapes

What are angles? What kinds of angles are there and how do they relate? Vertical angles, supplementary angles, complementary angles, corresponding angles, we cover them all in here!

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Types of Angles and Angle Relationships

Shapes! They're so fun. But they're even more fun when you know precisely how to define them. What's a rhombus? What's a parallelogram? Did you know that squares are rectangles? And both squares and rectangles are parallelograms? There's a whole hierarchy! Seriously, get into this stuff.

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Types of Quadrilaterals and Other Polygons

If a shape is made of straight line segments, the minimum number of sides it can have is three. And three sides make a triangle! I'm sure you knew that. But do you know all the types of triangles? Oh you do? Then what's a scalene triangle? Hah! I knew you were bluffing. You'd better watch this right away.

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Types of Triangles in Euclidean Geometry

Now we know about different kinds of triangles and their characteristics, so we should be able to look at two triangles and say whether they are similar, congruent, or unrelated. For more information on what that means and how to do it, check out this clip! It's chock-full of theorems.

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Proving Triangle Congruence and Similarity

We just went over a bunch of different theorems, but we need to do one more! It's kind of neat. I don't have anything else to say, just watch this, it's really short.

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The Triangle Midsegment Theorem

Enough of this two-dimensional, stuck in one plane rubbish! The real world has three spatial dimensions! Technically more, but we very clearly interact with three all the time, so it's time to start talking about three-dimensional shapes like pyramids and prisms and cylinders and cones, and the characteristics they possess.

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Special Lines in Triangles: Bisectors, Medians, and Altitudes

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Geometry #5

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