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Geometry: High School15 chapters | 160 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Did you ever wonder what the pyramids in Egypt have to do with math? Watch this video to find out where in math a pyramid comes into play. Also, learn how flat, 2-dimensional shapes also come into play.

First, what is a plane? It's not the type that flies overhead - the airplanes that transport people and things - but **planes** in math are flat surfaces that stretch out forever in all directions. It's like taking a piece of paper and imagining that the piece of paper never ended, that it has no edges.

Now, imagine punching all kinds of shapes out of our plane. Now, these shapes must have only straight edges, no curves of any kind. So, think of rectangles, squares, triangles, pentagons and the like; all of these flat shapes are pieces of a plane. These pieces are also called polygons because they have only straight edges.

When you connect several of these flat shapes and turn it into something 3-dimensional, then you have yourself a **polyhedron**. Defined, a polyhedron is a 3-dimensional object with flat, polygonal faces. What this means is that each side of the polyhedron is made up of one of our pieces from our plane. Each side is a polygon.

What do they look like? They can look similar to balls, except they have flat sides and edges and no curves. They can also look like ornaments that people hang up. Any 3-dimensional shape that you can create by gluing together polygons punched out of our plane is a polyhedron. Just remember that you have to glue all the pieces together; you can't have an open hole somewhere!

Where in real life will we see polyhedra? Here is where the pyramids of Egypt come into play. A pyramid has flat sides that are made up of polygons. The sides are triangles and the bottom is a square. That makes a pyramid a polyhedron!

Other real-world examples of polyhedra include various dice used in games. Most dice have flat sides, and when you roll them, whatever side is facing up is usually the side that tells you your next allowed move in the game. So, flat, polygonal sides for the 3-dimensional object makes them polyhedra!

If the room that you are sitting in has only flat walls, then you are sitting inside a polyhedron. All buildings that use only straight edges and no curves are polyhedra. As you can see, polyhedra are used everywhere in the world around us. So there are many applications of this type of object in the real world.

What have we learned? We've learned that a **plane** is a 2-dimensional flat surface that goes on forever. A **polyhedron** is a 3-dimensional object with flat, polygonal sides. These polygonal sides are shapes - specifically polygons - that have been punched out of a plane. There are no curves in a polyhedron, so think of triangles, squares, rectangles, pentagons and so on. Real-world applications of polyhedrons include pyramids, game dice and buildings.

When this lesson is done, you should be able to:

- Define what a plane is
- Recognize polyhedra as 3-dimensional objects without curves
- Identify polyhedra in the real word

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Geometry: High School15 chapters | 160 lessons

- Planes and the Polyhedron: Definition and Example 3:52
- Prisms: Definition, Area & Volume 6:12
- Pyramids: Definition, Area & Volume 7:43
- What Are Cylinders? - Definition, Area & Volume 5:09
- Cones: Definition, Area & Volume 8:59
- Spheres: Definition, Area & Volume 5:22
- Go to High School Geometry: Geometric Solids

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