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FeatureLesson Geometry Lesson Main Lesson 11-1 (For help, go to Lesson 1-3.) For each exercise, make a copy of the cube at the right. Shade the plane that contains the indicated points. 1. A, B, and C 2. A, C, and G 3. F, D, and G 4. the midpoints of AD CD, EH, and GH Space Figures and Cross Sections Check Skills Youll Need 11-1

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FeatureLesson Geometry Lesson Main Space Figures and Cross Sections Lesson 11-1 Homework 11-1

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FeatureLesson Geometry Lesson Main Space Figures and Cross Sections Lesson 11-1 Notes 11-1 A polyhedron is a three-dimensional figure whose surfaces are polygons. Each polygon is called a face. An edge is the segment that is the intersection of two faces. A vertex is the point that is the intersection of three or more edges.

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FeatureLesson Geometry Lesson Main How many vertices, edges, and faces of the polyhedron are there? List them. There are 10 vertices: Space Figures and Cross Sections Lesson 11-1 A, B, C, D, E, F, G, H, I, and J. There are 15 edges: AF, BG, CH, DI, EJ, AB, BC, CD, DE, EA, FG, GH, HI, IJ, and JF. There are 7 faces: pentagons: ABCDE and FGHIJ, and quadrilaterals: ABGF, BCHG, CDIH, DEJI, and EAFJ Quick Check Additional Examples 11-1 Identifying Vertices, Edges and Faces

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FeatureLesson Geometry Lesson Main Space Figures and Cross Sections Lesson 11-1 Notes 11-1 Euler is pronounced Oiler. Reading Math

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FeatureLesson Geometry Lesson Main Use Eulers Formula to find the number of edges on a solid with 6 faces and 8 vertices. F + V = E + 2Eulers Formula = E + 2Substitute the number of faces and vertices. 12 = ESimplify. A solid with 6 faces and 8 vertices has 12 edges. Space Figures and Cross Sections Lesson 11-1 Quick Check Additional Examples 11-1 Using Eulers Formula

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FeatureLesson Geometry Lesson Main Space Figures and Cross Sections Lesson 11-1 Notes 11-1 A net is a diagram of the surfaces of a three- dimensional figure that can be folded to form the three-dimensional figure. To identify a three-dimensional figure from a net, look at the number of faces and the shape of each face.

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FeatureLesson Geometry Lesson Main Use the pentagonal prism from Example 1 to verify Eulers Formula. Then draw a net for the figure and verify Eulers Formula for the two-dimensional figure. F + V = E + 2Eulers Formula Use the faces F = 7, vertices V = 10, and edges E = 15. Count the regions: F = 7 Space Figures and Cross Sections Lesson = Substitute the number of faces and vertices. Count the vertices: V = 18 Count the segments: E = 24 F + V = E + 1 Eulers Formula in two dimensions = Substitute. Draw a net. Quick Check Additional Examples 11-1 Verifying Eulers Formula

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FeatureLesson Geometry Lesson Main Space Figures and Cross Sections Lesson 11-1 Notes 11-1 A cross section is the intersection of a three- dimensional figure and a plane. The cross section is a triangle. The cross section is a rectangle.

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FeatureLesson Geometry Lesson Main Describe this cross section. The plane is parallel to the triangular base of the figure, so the cross section is also a triangle. Space Figures and Cross Sections Lesson 11-1 Quick Check Additional Examples 11-1 Describing a Cross Section

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FeatureLesson Geometry Lesson Main Draw and describe a cross section formed by a vertical plane intersecting the top and bottom faces of a cube. If the vertical plane is parallel to opposite faces, the cross section is a square. Sample: If the vertical plane is not parallel to opposite faces, the cross section is a rectangle. Space Figures and Cross Sections Lesson 11-1 Quick Check Additional Examples 11-1 Drawing a Cross Section

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FeatureLesson Geometry Lesson Main 1. Draw a net for the figure. Use Eulers Formula to solve. 2. A polyhedron with 12 vertices and 30 edges has how many faces? Space Figures and Cross Sections Lesson 11-1 Circle Check students drawings; rectangle. Sample: 3. A polyhedron with 2 octagonal faces and 8 rectangular faces has how many vertices? 4. Describe the cross section. 5. Draw and describe a cross section formed by a vertical plane cutting the left and back faces of a cube. Lesson Quiz 11-1

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FeatureLesson Geometry Lesson Main Lesson 11-1 (For help, go to Lesson 1-3.) For each exercise, make a copy of the cube at the right. Shade the plane that contains the indicated points. 1. A, B, and C 2. A, B, and G 3. A, C, and G 4. A, D, and G 5. F, D, and G 6. B, D, and G 7. the midpoints of AD CD, EH, and GH Space Figures and Cross Sections Check Skills Youll Need 11-1

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FeatureLesson Geometry Lesson Main Solutions Space Figures and Cross Sections Lesson Check Skills Youll Need 11-1

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