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Classifying Polygons and Three-Dimensional Figures

Learn to classify polygons and three-dimensional figures based on their properties, vertices, edges, bases, and cross-sections. Understand prisms, pyramids, and cylinders.

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Classifying Polygons and Three-Dimensional Figures

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  1. Warm Up Classify each polygon. 1.a polygon with three congruent sides 2. a polygon with six congruent sides and six congruent angles 3. a polygon with four sides and with opposite sides parallel and congruent equilateral triangle regular hexagon parallelogram

  2. Notes 12-1, 12-2 Three Dimensional Figures, Nets, and Surface Areas

  3. Three-Dimensional Figures • Solids • Face • Edge • Vertex

  4. Orthogonal Drawings

  5. Prisms and Pyramids • Named for their bases. • Cube

  6. edges: Example: Classifying Three-Dimensional Figures Classify the figure. Name the vertices, edges, and bases. cube vertices: A, B, C, D, E, F, G, H bases: ABCD, EFGH, ABFE, DCGH, ADHE, BCGF

  7. edges: Example: Classifying Three-Dimensional Figures Classify the figure. Name the vertices, edges, and bases. pentagonal pyramid vertices: A, B, C, D, E, F base: ABCDE

  8. A cross sectionis the intersection of a three-dimensional figure and a plane.

  9. A cross sectionis the intersection of a three-dimensional figure and a plane. Example: Describing Cross Sections of Three-Dimensional Figures Describe the cross section. The cross section is a point.

  10. Example: Describing Cross Sections of Three-Dimensional Figures Describe the cross section. The cross section is a pentagon.

  11. Example: Describe the cross section. The cross section is a hexagon.

  12. Example: Describe the cross section. The cross section is a triangle.

  13. Net • Diagram of the surface s of a 3-dimensional figure. Describe the three-dimensional figure that can be made from the given net.

  14. Example: Identifying a Three-Dimensional Figure From a Net Describe the three-dimensional figure that can be made from the given net.

  15. Prisms and Cylinders • Prisms and cylinders have 2 congruent parallel bases. • A lateral faceis not a base. • The edges of the base are called base edges. • A lateral edgeis not an edge of a base. • The lateral faces of a right prismare all rectangles. • An oblique prismhas at least one nonrectangular lateral face.

  16. An altitudeof a prism or cylinder is a perpendicular segment joining the planes of the bases. The height of a three-dimensional figure is the length of an altitude. Surface areais the total area of all faces of a three-dimensional figure. The lateral area of a prism is the sum of the areas of the lateral faces.

  17. Cylinders • The lateral surfaceof a cylinder is the curved surface that connects the two bases. • The axis of a cylinderis the segment with endpoints at the centers of the bases. • The axis of a right cylinderis perpendicular to its bases. • The axis of an oblique cylinderis not perpendicular to its bases. • The altitude of a right cylinder is the same length as the axis.

  18. triangular prism; vertices: A, B, C, D, E, F; edges: bases: ∆ABC and ∆DEF Lesson Quiz: Part I 1. Classify the figure. Name the vertices, edges, and bases.

  19. Lesson Quiz: Part II 2. Describe the three-dimensional figure that can be made from this net. square pyramid

  20. Lesson Quiz: Part III 3. Describe the cross section. a rectangle

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