1. Obj. 49 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. Extend midpoint and distance formulas to three dimensions

2. face edge vertex The flat 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. prism cylinder 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. 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 11. 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 12. To find the length of d, or (Pyth. Theorem) w h x d + = + = 2 2 2 2 2 2 w x h x d + + =2 2 2 2 w h d = + +2 2 2 d w h 13. Examples (round to the nearest tenth) 1. Find the length of the diagonal of a 3 in. by 4 in. by 5 in. rectangular prism. 2. Find the height of a rectangular prism with an 8 ft by 12 ft base and an 18 ft diagonal. = + + = 2 2 2 d 3 4 5 50 7.1 in. = + + = + = = 2 2 2 2 2 2 18 8 12 h 324 208 h h 116 h 116 10.8 ft. 14. space The set of point in all three dimensions. Instead of two coordinates, we need three coordinates to locate a point in space, so we now have an x-axis, a y-axis, and a z- axis. Example: Plot the point (3, 2, 4) 15. Example: Find the distance and midpoint between (6, 11, 3) and (4, 6, 12). Round to the nearest tenth if necessary. ( ) ( ) ( )= + + = + + = 2 2 2 d 4 2 6 11 12 3 4 25 81 110 10.5 ( ) + + + 6 4 11 6 3 12 M , , 2 2 2 M 5, 8.5, 7.5