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Understanding Polyhedrons and Their Properties in 3D Geometry

This chapter introduces essential vocabulary related to three-dimensional figures, focusing on polyhedrons. A polyhedron is defined as a solid with flat surfaces that enclose a single region of space. Key terms including faces, edges, and vertices are explained. The document also provides examples to help identify different polyhedra and their constituents, such as triangular pyramids, prisms, and other solids. Moreover, it discusses the concept of cross-sections and demonstrates how to determine the shape of cross-sections of various solids through examples, enhancing comprehension of geometric representations.

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Understanding Polyhedrons and Their Properties in 3D Geometry

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  1. Chapter 1.7 and 12.1 Thee-Dimensional Figures and their representations

  2. Vocabulary • Polyhedron – a solid with all flat surfaces that enclose a single region of space • Face – each flat surface of a polyhedron • Edges – the line segments where faces intersect • Vertex – the point where three or more edges intersect

  3. Identify Solids Example 1 A.Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.

  4. Identify Solids Example 1 B.Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.

  5. Identify Solids C.Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.

  6. A. Identify the solid. A. triangular pyramid B. pentagonal prism C. rectangular prism D. square pyramid

  7. B. Identify the solid. A. cone B. cylinder C. pyramid D. polyhedron

  8. C. Identify the solid. A. triangular prism B. triangular pyramid C. rectangular pyramid D. cone

  9. Concept

  10. Cross Section • A cross section is the intersection of a solid and a plane

  11. Identify Cross Sections of Solids Example 3 BAKERYA customer ordered a two-layer sheet cake. Determine the shape of each cross section of the cake below.

  12. Example 3 A solid cone is going to be sliced so that the resulting flat portion can be dipped in paint and used to make prints of different shapes. How should the cone be sliced to make prints in the shape of a triangle? A. Cut the cone parallel to the base. B. Cut the cone perpendicular to the base through the vertex of the cone. C. Cut the cone perpendicular to the base, but not through the vertex. D. Cut the cone at an angle to the base.

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