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7-1 Three-Dimensional Figures

Geogebra Three-dimensional figures Pyramid Pyramid Explode Prism Net Prism Net (2)

Video Tutor Help Naming a three-dimensional figure Drawing a net Finding surface areas of prisms using a net Finding surface areas of cylinders using a net Finding the volumes of prisms Finding the volumes of cylinders

Video Tutor Help Naming a three-dimensional figureNaming a three-dimensional figure (7-1) Drawing a base plan for a 3-D figureDrawing a base plan for a 3-D figure (7-1) Drawing top, front, and right viewsDrawing top, front, and right views (7-1) Draw the 3D figure

Worksheets Daily Notetaking Guide Worksheets Version A Practice, Guided Problem Solving Lesson 7-1 Practice 7-1 Guided Problem Solving 7-1

Vocabulary Practice Vocabulary 7A: Graphic Organizer Vocabulary 7B: Reading Comprehension Vocabulary 7C: Reading/Writing Math Symbols Vocabulary 7D: Visual Vocabulary Practice Vocabulary 7E: Vocabulary C Vocabulary 7F: Vocabulary Review Puzzle Vocabulary (Electronic) Flash Cards Geometry

Additional Lesson Examples Step-by-Step Examples Lesson 7-1

Lesson Readiness Lesson Quiz Problem of the Day Lesson 7-1

Three-dimensional figures Prism Net Prism Net (2)

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 called a base.

Pyramid Pyramid Explode Three-dimensional figures Prism Net Prism Net (2)

Additional Example 1: 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. A.

Additional Example 1: Naming Prisms and Pyramids There is one base, and it is a triangle. There are three triangular faces. The figure is a triangular pyramid. Describe the bases and faces of the figure. Then name the figure. B.

Additional Example 1: Naming Prisms and Pyramids There are two bases, and they are both hexagons. There are six rectangular faces. The figure is a hexagonal prism. Describe the bases and faces of the figure. Then name the figure. C.

Partner Share! Example 1 There are two bases and they are both triangles. There are three rectangular faces. The figure is a triangular prism. Describe the bases and faces of the figure. Then name the figure. A.

Partner Share! Example 1 There are two rectangular bases. The figure is a rectangular prism. Describe the bases and faces of the figure. Then name the figure. B. There are four other rectangular faces.

Describe the bases and faces of the figure. Then name the figure. C. Partner Share! Example 1 There are two octagonal bases. The figure is an octagonal prism. There are eight rectangular faces.

Other three-dimensional figures include cylinders and cones. These figures are not polyhedrons because they are not made of faces that are all polygons.

You can use properties to classify three- dimensional figures.

Classify each figure as a polyhedron or not a polyhedron. Then name the figure. A. Additional Example 2: 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.

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

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

Partner Share! Example 2 Classify each figure as a polyhedron or not a polyhedron. Then name the figure. A. 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.

Partner Share! Example 2 Classify each figure as a polyhedron or not a polyhedron. Then name the figure. B. 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.

Partner Share! Example 2 Classify each figure as a polyhedron or not a polyhedron. Then name the figure. C. 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.

Name the geometric figure. The figure is a sphere. LESSON 7-1 Three-Dimensional Figures Additional Examples

Example 1-1a Identify the solid. Name the bases, faces, edges, and vertices. Answer: This figure has two parallel congruent bases that are rectangles, GHJK and LMNP, so it is a rectangular pyramid. faces: GHJK, LMNP, GHML, HJNM, JKPN, GKPL edges: vertices: G, H, J, K, L, M, N, P Identify Prisms and Pyramids

Example 1-1b Identify the solid. Name the bases, faces, edges, and vertices. Answer: This figure has one triangular base, DEF, so it is a triangular pyramid. faces: DEF, DEG, DFG, EFG edges: vertices: D, E, F, G Identify Prisms and Pyramids

Example 1-1c Identify each solid. Name the bases, faces, edges, and vertices. a. Answer: rectangular pyramid base: BCDE faces: ABC, ACD, ADE, AEB, BCDE edges: vertices: A, B, C, D, E

Example 1-1d Identify each solid. Name the bases, faces, edges, and vertices. b. Answer: rectangular prism bases: GHJK, LMNP or GKPL, HJNM or GHML, KJNP faces: GHJK, LMNP, GHML, HJNM, JKPN, GKPL edges: vertices: G, H, J, K, L, M, N, P

Example 1-2a Identify a diagonal and name all segments that are skew to it. Answer: is a diagonal because vertex Q and vertex W do not intersect any of the same faces; Identify Diagonals and Skew Lines

Example 1-2b Identify a diagonal and name all segments that are skew to it. Answer:

Example 4-1a Identify the solid. Name the number and shapes of the faces. Then name the number of edges and vertices. Answer: The figure has two parallel congruent bases that are octagons, so it is an octagonal prism. The other faces are rectangles. It has a total of 10 faces, 24 edges, and 16 vertices. Identify Prisms and Pyramids

Example 4-2a Identify the solid. Name the number and shapes of the faces. Then name the number of edges and vertices. Answer: The figure has one base that is a rectangle, so it is a rectangular pyramid. The other faces are triangles. It has a total of 5 faces, 8 edges, and 5 vertices. Identify Prisms and Pyramids

Example 4-2b Identify the solid. Name the number and shapes of the faces. Then name the number of edges and vertices. Answer: pentagonal pyramid; 1 pentagonal base, 5 triangular faces, 10 edges, and 6 vertices

Draw a pentagonal prism. LESSON 7-1 Step 1 Draw a pentagon. Step 2 Draw a second pentagon congruent to the first. Step 3 Connect the vertices. Use dashed lines for hidden edges. Three-Dimensional Figures Additional Examples

Lesson Review: Part I Describe the bases and faces of each figure. Then name each figure. Two pentagonal bases, 5 rectangular faces; pentagonal prism One square base, 4 triangular faces; square pyramid 1. 2.

Lesson Review: Part II Classify each figure as a polyhedron or not a polyhedron. Then name the figure. polyhedron, rectangular prism polyhedron, triangular prism 3. 4.