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Construction Geometry

Construction Geometry. Geometric Solid Basics Prisms Pyramids Cylinders Cones Spheres. Geometric Solids. Geometric solids are three-dimensional geometric figures. Our lessons will focus on right solids and will include: Prisms Pyramids Cones Cylinders Spheres.

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Construction Geometry

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  1. Construction Geometry Geometric Solid Basics Prisms Pyramids Cylinders Cones Spheres

  2. Geometric Solids • Geometric solids are three-dimensional geometric figures. • Our lessons will focus on right solids and will include: • Prisms • Pyramids • Cones • Cylinders • Spheres

  3. Geometric Solids • Geometric solids can be either “right” or “oblique”. • Right solids have a vertical central axis while oblique solids (shown below) do not.

  4. Geometric Solids • Our lessons will deal only with “right” solids. • Right solids have a vertical central axis.

  5. Prisms • Prisms • Rectangular sides • 2 congruent parallel bases • Named by the shape of the base • Rectangular bases = “Rectangular Prism”

  6. Prisms • These are a few examples of prisms: • Triangular Prism • Rectangular Prism • Pentagonal Prism

  7. Application • An octagonal concrete form is an example of an octagonal prism.

  8. Application • This is a concrete form used to pour octagonal solids.

  9. Application • They can be stacked with great stability compared to most other shapes, and are used in construction.

  10. Application • Concrete solids can be used as a withholding wall for soil.

  11. Application • The solids (octagonal prisms) are used as a withholding wall.

  12. Pyramids • Pyramids are solid figures with a polygonal base and triangular sides that meet in a single point, called a vertex.

  13. Pyramids • Pyramids are usually identified as ones pictured in Egyptian times, with a square base and 4 triangular sides. • But pyramids can have any polygon base, such as triangles, rectangles, and pentagons.

  14. Pyramids • These are a few examples of pyramids: • Triangular Pyramid • Rectangular Pyramid • Pentagonal Pyramid

  15. Prisms and Pyramids • Prisms are named by their 2 congruent parallel bases. • Pyramids are named by their single base.

  16. Polyhedron • “Poli” = many “hedron” = face • A polyhedron is a 3-D figure with polygonal faces. • Prisms and pyramids are polyhedrons.

  17. Top Right Side Front Faces • The faces of a polyhedron are polygons and include the bases. • A rectangular prism has 6 faces: Top, Bottom, Front, Back, Right, Left Sides. Top Bottom Front Back Right Left

  18. Faces • A hexagonal pyramid has 7 faces: a hexagonal base and 6 triangular sides.

  19. Edges • Edges are segments where the sides meet. • A rectangular prism has 12 edges. • A hexagonal pyramid has 12 edges.

  20. Vertices • Vertices are where the edges meet at a point. • A rectangular prism has 8 vertices. • A hexagonal pyramid has 7 vertices.

  21. Practice #1 • Determine the name and number of edges for the given figure. • Trapezoidal Prism, 12 edges

  22. Practice #2 • Determine the number of faces and vertices for the Triangular Prism. • 5 faces, 6 vertices

  23. Cylinder • A cylinder is a solid figure with 2 congruent, parallel, circular bases. Campbells

  24. Cones • Cones are solids that have a circular base and a vertex.

  25. Sphere • A sphere is a solid comprised of the set of all points in space equidistant from a given point.

  26. Sphere • Spheres do not have faces, edges, or vertices.

  27. Practice #3 • Name each figure.

  28. Practice #3

  29. Practice #4 • Determine the number of vertices, faces, and edges for the octagonal prism.

  30. Practice #4 • Vertices = 8 + 8 = 16 • Faces = 8 + 2 = 10 • Edges = 8 + 8 + 8 = 24

  31. Practice #5 • List the faces, edges, and vertices of the rectangular prism. • Faces = ABC, EFG, ABF, DCG, BFG, AEH • Edges = AB, BC, CD, AD AE, BF, CG, DH EF, FG, GH, HE • Vertices = A, B, C, D, E, F, G, H B C D A F G E H

  32. Practice & Assessment Materials • You are now ready for the practice problems for this lesson. • After completion and review, take the assessment for this lesson.

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