VIEWS: 67 PAGES: 21 POSTED ON: 11/3/2009
Introduction to Three-Dimensional 9-1 Figures Warm Up Problem of the Day Lesson Presentation Course 2 Introduction to Three-Dimensional 9-1 Figures Warm Up Identify each two-dimensional figure described. 1. four sides that are all congruent rhombus 2. six sides hexagon 3. four sides with parallel opposite sides parallelogram 4. four right angles and four congruent sides square Course 2 Introduction to Three-Dimensional 9-1 Figures Problem of the Day If the figure shown is folded into a cube so that six is on the top, what number would be on the bottom? 2 Course 2 Introduction to Three-Dimensional 9-1 Figures Learn to identify various threedimensional figures. Course 2 Introduction to Three-Dimensional 9-1 Figures Lesson Title Here Insert Vocabulary face edge vertex base polyhedron prism pyramid lateral surface cylinder cone sphere hemisphere Course 2 Introduction to Three-Dimensional 9-1 Figures Three-dimensional figures, or solids, have length, width, and height. A flat surface of a solid is a face. An edge is where two faces meet, and a vertex is where three or more edges meet. The face that is used to classify a solid is a base. The surfaces of a three-dimensional figure determine the type of solid it is. A polyhedron is a three-dimensional figure whose surfaces, or faces, are all polygons. Prisms and pyramids are two types of polyhedrons. Course 2 Introduction to Three-Dimensional 9-1 Figures Prisms A prism is a polyhedron that has two parallel congruent bases. The bases can be any polygon. The other faces are parallelograms. A cube is a special prism whose faces are all congruent squares. Course 2 Introduction to Three-Dimensional 9-1 Figures Pyramids A pyramid is a polyhedron that has one base. The base can any polygon. The other faces are triangles. A regular tetrahedron is a special pyramid whose faces are all congruent equilateral triangles. Course 2 Introduction to Three-Dimensional 9-1 Figures Prisms and polygons are named by the shapes of their bases. Course 2 Introduction to Three-Dimensional 9-1 Figures Additional Example 1A: Naming Prisms and Pyramids Identify the base or bases of the solid. Then name the solid. A. There are two bases, and they are both octagons. The other faces are parallelograms. The figure is an octagonal prism. Course 2 Introduction to Three-Dimensional 9-1 Figures Additional Example 1B: Naming Prisms and Pyramids Identify the base or bases of the solid. Then name the solid. B. There is one base, and it is a pentagon. The other faces are triangles. The figure is a pentagonal pyramid. Course 2 Introduction to Three-Dimensional 9-1 Figures Try This: Example 1A Identify the base or bases of the solid. Then name the solid. A. There are two bases and they are both triangles. The other faces are parallelograms. The figure is a triangular prism. Course 2 Introduction to Three-Dimensional 9-1 Figures Try This: Example 1B Identify the base or bases of the solid. Then name the solid. B. All faces are congruent squares. The figure is a cube. Course 2 Introduction to Three-Dimensional 9-1 Figures Other three-dimensional figures include cylinders, cones, and spheres. These figures are different from polyhedrons because they each have a curved surface and their bases are not polygons. The curved surface of a cylinder or a cone is called a lateral surface. Course 2 Introduction to Three-Dimensional 9-1 Figures 2 bases A cylinder has two parallel, congruent circular bases connected by a lateral surface. Lateral surface A cone has one circular base 1 base Lateral surface and a lateral surface. The lateral surface of a cone comes to a point called its Vertex vertex. Course 2 Introduction to Three-Dimensional 9-1 Figures A sphere has only one surface, which is curved, and has no base. All of the points on the surface are the same distance from the center of the sphere. A plane that intercepts a sphere through its center divides the sphere into two different halves, or hemispheres. Top hemisphere Bottom hemisphere Course 2 Introduction to Three-Dimensional 9-1 Figures Additional Example 2A: Identifying Combinations of Solids Tell what solids make up each figure. A. The figure is made up of a rectangular pyramid and a rectangular prism. Course 2 Introduction to Three-Dimensional 9-1 Figures Additional Example 2B: Identifying Combinations of Solids Tell what solids make up each figure. B. The figure is made up of a hemisphere and a cone. Course 2 Introduction to Three-Dimensional 9-1 Figures Try This: Example 2A Tell what solids make up each figure. A. The figure is made up of a cone and a cylinder. Course 2 Introduction to Three-Dimensional 9-1 Insert Lesson Title Here Figures Try This: Example 2B Tell what solids make up each figure. B. The figure is made up of a cylinder and a hemisphere. Course 2 Introduction to Three-Dimensional 9-1 Figures Lesson Title Here Insert Lesson Quiz Identify the type of each prism or pyramid. 1. square pyramid 2. pentagonal prism Identify the figure described. 3. two congruent circular faces connected by a curved surface cylinder 4. one circular face and a curved lateral surface that comes to a point called a vertex cone Course 2