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Solid Geometry
The student is able to (I can):
Classify three-dimensional figures according to their
properties.
Use nets and cross sections to analyze three-dimensional
figures.
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face
edge
vertex
The flat polygonal surface on a three-dimensional figure.
The segment that is the intersection of two faces.
The point that is the intersection of three or more edges.
faceedge
vertex
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polyhedron
prism
cylinder
A three-dimensional figure composed of polygons. (plural
polyhedra)
Two parallel congruent polygon basesconnected by faces that are
parallelograms.
Two parallel congruent circular bases and a curved surface that
connects the bases.
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pyramid
cone
A polygonal base with triangular faces that meet at a common
vertex.
A circular base and a curved surface that connects the base to a
vertex.
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A cube is a prism with six square faces. Other prisms and
pyramids are named for the shape of their bases.
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net A diagram of the surfaces of a three-dimensional figure that
can be folded to form the figure.
To identify a figure from a net, look at the number of faces and
the shape of each face.
This is the net of a cube because it has six squares.
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Examples Describe the three-dimensional figure from the net.
1.
2.
Triangular Pyramid
Cylinder
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cross section The intersection of a three-dimensional figure and
a plane.
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Examples Describe the cross sections:
1.
2.
A hexagon
A triangle
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Eulers Formula
For any polyhedron with V vertices, E edges, and F faces, V E +
F = 2.
Example: If a given polyhedron has 12 vertices and 18 edges, how
many faces does it have?
+ =
+ =
=
V E F 2
12 18 F 2
F 8
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The Platonic solids are made up of regular polygons.
Name# of faces
Polygon Picture
Tetrahedron 4Equilateral triangles
Octahedron 8Equilateral triangles
Icosahedron 20Equilateral triangles
Hexahedron (cube)
6 Squares
Dodecahedron 12 Pentagons
