### Teacher Guide to Shapes

#### Our world is filled with a variety of shapes - each of which falls into two broad types: plane shapes and solid shapes. Knowing your shapes is the first step to understanding geometry and spatial sense. Of primary consideration in differentiating shapes is understanding the differences that exist in proportion, symmetry, and general coordinates.

PLANE SHAPES

Any figure that can be drawn two-dimensionally is referred to as a plane shape. This means that a plane shape will have the dimensions of length and width but they lack the third dimension of height. Most are considered "polygons" - this means that they have straight sides. For example, a circle or oval cannot be called a polygon because it has curved edges.

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Other than curvilinear shapes (such as circles, semi-circles, and ovals), plane shapes are characterized specifically by the number of sides they have:

3. Triangle: three sides
5. Pentagon: five sides
6. Hexagon: six sides
7. Heptagon: seven sides
8. Octagon: eight sides
9. Nonagon: nine sides
10. Decagon: ten sides
11. Undecagon: eleven sides
12. Dodecagon: twelve sides

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SOLID SHAPES

Solid shapes are those that are three-dimensional. This means that they possess length, width, and height (sometimes called depth). These surfaces are commonly referred to as "faces".

There are two primary forms of solid shape: prisms (meaning they have flat tops and flat bottoms) and pyramids (indicating a flat bottom and a pointy top). When all the edges of a solid shape are straight, it is referred to a polyhedron, or "many faced". It is then classified by the number of faces it has:

4. Tetrahedron: four faces
5. Pentahedron: five faces
6. Hexahedron: six faces
7. Heptahedron: seven faces
8. Octahedron: eight faces
9. Nonahedron: nine faces
10. Decahedron: ten faces
11. Undecahedron: eleven faces
12. Dodecahedron: twelve faces

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There can be no triahedron because it is impossible to create a three-dimensional object with only three straight faces.

There are also several types of solid shapes that are not polyhedron; these include:

- Spheres: meaning shaped like a ball

- Cones: round objects with flat bottoms and pointy tops

- Cylinders: round objects with flat bottoms and flat tops

- Ellipsoids: shaped like a watermelon

WHY DOES THE SHAPE MATTER?
Each specific shape has various methods for determining its geometry - things like perimeter, surface area, volume, etc. These calculations are commonly unique for the specific shape of the object or figure.

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