Obj. 42 Solid Geometry
- 1. 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.
- 2. 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. face edge vertex•
- 3. polyhedron prism cylinder A three-dimensional figure composed of polygons. (plural polyhedra) Two parallel congruent polygon bases connected by faces that are parallelograms. Two parallel congruent circular bases and a curved surface that connects the bases.
- 4. 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.
- 5. A cube is a prism with six square faces. Other prisms and pyramids are named for the shape of their bases.
- 6. 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.
- 7. Examples Describe the three-dimensional figure from the net. 1. 2. Triangular Pyramid Cylinder
- 8. cross section The intersection of a three-dimensional figure and a plane.
- 9. Examples Describe the cross sections: 1. 2. A hexagon A triangle
- 10. Euler’s 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
- 11. The Platonic solids are made up of regular polygons. Name # of faces Polygon Picture Tetrahedron 4 Equilateral triangles Octahedron 8 Equilateral triangles Icosahedron 20 Equilateral triangles Hexahedron (cube) 6 Squares Dodecahedron 12 Pentagons