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Unit 8 Lesson 1 – Explore Solids

Unit 8 Lesson 1 – Explore Solids. Polyhedron:. A solid that is bounded by polygons. Non-Polyhedron:. An edge that isn’t a polygon. No Curves!. Prism:. Polyhedron with two parallel, congruent bases. Named after its base. Triangular Prism. Hexagonal Prism. Pyramid:.

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Unit 8 Lesson 1 – Explore Solids

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  1. Unit 8 Lesson 1 – Explore Solids

  2. Polyhedron: A solid that is bounded by polygons

  3. Non-Polyhedron: An edge that isn’t a polygon No Curves!

  4. Prism: Polyhedron with two parallel, congruent bases Named after its base. Triangular Prism Hexagonal Prism

  5. Pyramid: Polyhedron with one base. Named after its base. Rectangular Pyramid Pentagonal Pyramid

  6. Base: Polygon the solid is named after. Hexagon Rectangle

  7. Lateral Face: Parallelograms or triangles on the sides of the solid

  8. Convex: Any two points on its surface can be connected by a segment that lies entirely inside or on the solid (rubber band)

  9. A side of the solid goes inward Concave:

  10. Cross Section: Intersection of a plane and a solid

  11. Regular: All of the faces are congruent regular polygons

  12. Platonic Solids: Regular Polyhedra, only 5. Named after how many polygons they have containing the shape

  13. Regular Tetrahedron: 4 polygons

  14. Cube: 6 polygons

  15. Regular Octahedron: 8 polygons

  16. Regular Dodecahedron: 12 polygons

  17. Regular Icosahedron: 20 polygons

  18. Polygons containing the solid Faces: Ex: Hex ABCDFE

  19. Polygons containing the solid Faces: Ex: Hex ABCDFE Quad EFKL

  20. Where two polygons meet to form a line Edges: Ex:

  21. Where 3 polygons meet to form a point Vertex: (the corners) Ex:

  22. Euler’s Theorem: Faces + Vertices = Edges + 2 F + V = E + 2

  23. 1. Tell whether the solid is a polyhedron. If it is, find the number of faces, vertices, and edges. Polyhedron: YES or NO Faces: ___________ Vertices: _________ Edges: ___________ 6 6 10 F + V = E + 2 6 + 6 = 10 + 2 12 = 12

  24. 1. Tell whether the solid is a polyhedron. If it is, find the number of faces, vertices, and edges. Polyhedron: YES or NO Faces: ___________ Vertices: _________ Edges: ___________ 6 8 12 F + V = E + 2 6 + 8 = 12 + 2 14 = 14

  25. 1. Tell whether the solid is a polyhedron. If it is, find the number of faces, vertices, and edges. Polyhedron: YES or NO Faces: ___________ Vertices: _________ Edges: ___________

  26. 2. Use Euler’s Theorem to find the value of n. F + V = E + 2 n + 8 = 12 + 2 n + 8 = 14 n = 6

  27. 2. Use Euler’s Theorem to find the value of n. F + V = E + 2 5 + 6 = n + 2 11 = n + 2 9 = n

  28. 2. Use Euler’s Theorem to find the value of n. F + V = E + 2 8 + n = 18 + 2 8 + n = 20 n = 12

  29. 3. Identify the base of the polyhedron, then name the given shape. Hexagon Base: ____________ Shape: __________________ Hexagonal Pyramid

  30. 3. Identify the base of the polyhedron, then name the given shape. Rectangle Base: ____________ Shape: __________________ Rectangular Prism

  31. 3. Identify the base of the polyhedron, then name the given shape. Triangle Base: ____________ Shape: __________________ Triangular Prism

  32. 3. Identify the base of the polyhedron, then name the given shape. Rectangle Base: ____________ Shape: __________________ Rectangular Pyramid

  33. 3. Identify the base of the polyhedron, then name the given shape. Hexagon Base: ____________ Shape: __________________ Hexagonal Prism

  34. 3. Identify the base of the polyhedron, then name the given shape. Heptagon Base: ____________ Shape: __________________ Heptagonal Pyramid

  35. Determine if the solid is convex or concave. CONVEX or CONCAVE

  36. Determine if the solid is convex or concave. CONVEX or CONCAVE

  37. Determine if the solid is convex or concave. CONVEX or CONCAVE

  38. Describe the cross section formed by the intersection of the plane and the solid. pentagon

  39. Describe the cross section formed by the intersection of the plane and the solid. circle

  40. Describe the cross section formed by the intersection of the plane and the solid. triangle

  41. HW Problems #31 Ans: D

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