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8-7 Introduction to Three-Dimensional Figures Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

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8-7 Introduction to Three-Dimensional Figures Warm Up Identify each two-dimensional figure described. 1. four sides that are all congruent 2. six sides 3. four sides with parallel opposite sides 4. four right angles and four congruent sides rhombus hexagon parallelogram square

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8-7 Introduction to Three-Dimensional Figures Problem of the Day If the figure shown is folded into a cube so that 6 is on the top, what number would be on the bottom? 2

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8-7 Introduction to Three-Dimensional Figures Prep for MA.7.G.2.1 Justify and apply formulas for surface area and volume of pyramids, prisms, cylinders, and cones. Review of MA.5.G.3.1 Sunshine State Standards

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8-7 Introduction to Three-Dimensional Figures Vocabulary face edge polyhedron vertex base prism pyramid cylinder cone sphere

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8-7 Introduction to Three-Dimensional Figures Three-dimensional figures have three dimensions: length, width, and height. A flat surface of a three-dimensional figure is a face. An edge is where two faces meet. A polyhedron is a three-dimensional figure whose faces are all polygons. A vertex of a polyhedron is a point where three or more edges meet. The face that is used to name a polyhedron is a base. A prism has two bases, and a pyramid has one.

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8-7 Introduction to Three-Dimensional Figures

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8-7 Introduction to Three-Dimensional Figures Identify the bases and faces of the figure. Then name the figure. Additional Example 1A: Naming Prisms and Pyramids There are two octagonal bases. The figure is an octagonal prism. There are eight rectangular faces.

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8-7 Introduction to Three-Dimensional Figures Additional Example 1B: Naming Prisms and Pyramids There is one base, and it is a pentagon. There are five triangular faces. The figure is a pentagonal pyramid. Identify the bases and faces of the figure. Then name the figure.

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8-7 Introduction to Three-Dimensional Figures Additional Example 1C: Naming Prisms and Pyramids There is one base, and it is a triangle. There are three triangular faces. The figure is a triangular pyramid. Identify the bases and faces of the figure. Then name the figure.

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8-7 Introduction to Three-Dimensional Figures Additional Example 1D: Naming Prisms and Pyramids There are two bases, and they are both hexagons. There are six rectangular faces. The figure is a hexagonal prism. Identify the bases and faces of the figure. Then name the figure.

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8-7 Introduction to Three-Dimensional Figures Check It Out: Example 1A There are two bases and they are both triangles. There are three rectangular faces. The figure is a triangular prism. Identify the bases and faces of the figure. Then name the figure.

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8-7 Introduction to Three-Dimensional Figures Check It Out: Example 1B All faces and bases are congruent squares. The figure is a cube. Identify the bases and faces of the figure. Then name the figure.

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8-7 Introduction to Three-Dimensional Figures Other three-dimensional figures include cylinders, cones, and spheres. These figures are not polyhedrons because they are not made of faces that are all polygons.

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8-7 Introduction to Three-Dimensional Figures You can use properties to classify three- dimensional figures.

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8-7 Introduction to Three-Dimensional Figures Classify each figure as a polyhedron or not a polyhedron. Then name the figure. Additional Example 2A: Classifying Three- Dimensional Figures The faces are all polygons, so the figure is a polyhedron. There is one rectangular base for each figure. The figure is made up of a rectangular pyramid and a rectangular prism.

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8-7 Introduction to Three-Dimensional Figures There is one circular base. Classify each figure as a polyhedron or not a polyhedron. Then name the figure. Additional Example 2B: Classifying Three- Dimensional Figures The faces are not all polygons, so the figure is not a polyhedron. The figure is a cone.

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8-7 Introduction to Three-Dimensional Figures There are two circular bases. Classify each figure as a polyhedron or not a polyhedron. Then name the figure. Additional Example 2C: Classifying Three- Dimensional Figures The faces are not all polygons, so the figure is not a polyhedron. The figure is a cylinder.

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8-7 Introduction to Three-Dimensional Figures Check It Out: Example 2A Classify each figure as a polyhedron or not a polyhedron. Then name the figure. There is one circular base for the top figure and two circular bases for the bottom figure. The faces are not all polygons, so the figure is not a polyhedron. The figure is made up of a cylinder and a cone.

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8-7 Introduction to Three-Dimensional Figures Check It Out: Example 2B Classify each figure as a polyhedron or not a polyhedron. Then name the figure. There are two triangular bases for the figure. The faces are all polygons, so the figure is a polyhedron. The figure is a triangular prism.

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8-7 Introduction to Three-Dimensional Figures Check It Out: Example 2C Classify each figure as a polyhedron or not a polyhedron. Then name the figure. There is one square base for the figure. The faces are all polygons, so the figure is a polyhedron. The figure is a square pyramid.

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8-7 Introduction to Three-Dimensional Figures Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

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8-7 Introduction to Three-Dimensional Figures Lesson Quiz: Part I Identify the bases and faces of each figure. Then name each figure. Two pentagon bases, 5 rectangular faces; pentagonal prism One square base, 4 triangular faces; square pyramid 1. 2.

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8-7 Introduction to Three-Dimensional Figures Lesson Quiz: Part II Classify each figure as a polyhedron or not a polyhedron. Then name the figure. polyhedron, rectangular prism polyhedron, triangular prism 3. 4.

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8-7 Introduction to Three-Dimensional Figures 1. Identify the bases and faces, and then the name of the given figure. A. pentagon; triangles; pentagonal prism B. hexagon; triangles; hexagonal prism C. pentagon; triangles; pentagonal pyramid D. hexagon; triangles; hexagonal pyramid Lesson Quiz for Student Response Systems

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8-7 Introduction to Three-Dimensional Figures 2. Identify the bases and faces, and then the name of the given figure. A. pentagon; triangles; pentagonal pyramid B. heptagon; triangles; heptagonal pyramid C. pentagon; rectangles; pentagonal prism D. heptagon; rectangles; heptagonal prism Lesson Quiz for Student Response Systems

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8-7 Introduction to Three-Dimensional Figures 3. Classify the figure as a polyhedron or not a polyhedron, and then name the given figure. A. polyhedron; pentagonal prism B. polyhedron; pentagonal pyramid C. not a polyhedron; cylinder D. not a polyhedron; cone Lesson Quiz for Student Response Systems

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8-7 Introduction to Three-Dimensional Figures 4. Classify the figure as a polyhedron or not a polyhedron, and then name the given figure. A. polyhedron; heptagonal prism B. polyhedron; nonagonal pyramid C. not a polyhedron; cylinder D. not a polyhedron; cone Lesson Quiz for Student Response Systems

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