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Geometry Representations of Three-Dimensional Figures

Geometry Representations of Three-Dimensional Figures. Warm Up. Find the two numbers. The sum of two numbers is 30. The difference between 2 times the first number and 2 times the second number is 20 .

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Geometry Representations of Three-Dimensional Figures

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  1. GeometryRepresentations of Three-Dimensional Figures CONFIDENTIAL

  2. Warm Up • Find the two numbers. • The sum of two numbers is 30. The difference between 2 times the first number and 2 times the second number is 20. • The difference between the first number and the second number is 7. When the second number is added to 4 times the first number, the result is 38. • The second number is 5 more than the first number. Their sum is 5. • x = 20; y = 10 • x = 7; y = 2 • 3) x = 5; y = 0 CONFIDENTIAL

  3. Representations of Three-Dimensional Figures There are many ways to represent a three-dimensional object. An orthographic drawing shows six different views of an object: top, bottom, front, back, left side, and right side. Top Back Front Right Left Bottom CONFIDENTIAL

  4. Drawing Orthographic Views of an Object Draw all six orthographic views of the given object. Assume there are no hidden cubes. Top: Bottom: Back: Front: Left: Right: CONFIDENTIAL

  5. Now you try! 1) Draw all six orthographic views of the given object. assume there are no hidden cubes. CONFIDENTIAL

  6. Isometric drawing is a way to show three sides of a figure from a corner view. You can use isometric dot paper to make an isometric drawing. This paper has diagonal rows of dots that are equally spaced in a repeating triangular pattern. CONFIDENTIAL

  7. Drawing an isometric View of an Object Draw an isometric view of the given object. assume there are no hidden cubes. CONFIDENTIAL

  8. Now you try! 2) Draw an isometric view of the given object. assume there are no hidden cubes. CONFIDENTIAL

  9. In a perspective drawing, nonvertical parallel lines are drawn so that they meet at a point called a vanishing point. Vanishing point are located on a horizontal line called the horizon. A one-point perspective drawing contains one vanishing points. A two-point perspective drawing contains two vanishing points. Vanishing point s Vanishing point one-point perspective two-point perspective CONFIDENTIAL

  10. Drawing an Object in Perspective 3 A) Draw a cube in one-point perspective. Draw a horizontal line to represent the horizon. Mark a vanishing point on the horizon. This is the front of the cube. From each corner of the square, lightly draw dashed segments to the vanishing point. Next page  CONFIDENTIAL

  11. Lightly draw a smaller square with vertices on the dashed segments. This is the back of the cube. Draw the edges of the cube, using dashed segments for hidden edges. Erase any segments that are not part of the cube. Next page  CONFIDENTIAL

  12. B) Draw a rectangular prism in two-point perspective. From each endpoint of the segment, lightly draw dashed segments to each vanishing point. Draw two vertical segments connecting the dashed lines. These are other vertical edges of the prism. Draw a horizontal line to represent the horizon. Mark two vanishing points on the horizon. Then draw a vertical segment below the horizon and between the vanishing points. This is the front edge of the prism. Next page  CONFIDENTIAL

  13. Lightly draw dashed segments from each endpoint of the two vertical segments to the vanishing points. Draw the edges of the prism, using dashed lines for hidden edges. Erase any lines that are not part of the prism. CONFIDENTIAL

  14. Now you try! 3 a) Draw the block letter L in one-point perspective. b) Draw the block letter L in two-point perspective. CONFIDENTIAL

  15. Relating Different Representations of an Object 4) Determine whether each drawing represents the given object. Assume there are no hidden cubes. B A No; the figure in the drawing is made up of four cubes, and the object is made up of only three cubes. Yes; the drawing is a one-point perspective view of the object. Next page  CONFIDENTIAL

  16. C D Top Back Right Left Front Bottom No; the cubes that share a face in the object do not share a face in the drawing. Yes; the drawing shows the six orthographic views of the object. CONFIDENTIAL

  17. Now you try! 4) Determine whether drawing represents the given object. Assume there are no hidden cubes. Top Back Front Right Left Bottom CONFIDENTIAL

  18. Now some problems for you to practice ! CONFIDENTIAL

  19. Assessment 1) In a(n) ? Drawing, the vanishing point are located on the horizon. (orthographic, isometric, or perspective) • perspective CONFIDENTIAL

  20. 2)Draw all six orthographic views of the each object. Assume there are no hidden cubes. a) b) CONFIDENTIAL

  21. 3) Draw an isometric view of the given object. assume there are no hidden cubes. b) a) CONFIDENTIAL

  22. 4) Draw each object in one-point and two-point perspectives. Assume there are no hidden cubes. a) Rectangular prism b) block letter CONFIDENTIAL

  23. 5) Determine whether each drawing represents the given object. Assume there are no hidden cubes. a) b) c) CONFIDENTIAL

  24. Let’s review CONFIDENTIAL

  25. Representations of Three-Dimensional Figures There are many ways to represent a three-dimensional object. An orthographic drawing shows six different views of an object: top, bottom, front, back, left side, and right side. Top Back Front Right Left Bottom CONFIDENTIAL

  26. Drawing Orthographic Views of an Object Draw all six orthographic views of the given object. Assume there are no hidden cubes. Top: Bottom: Back: Front: Left: Right: CONFIDENTIAL

  27. Isometric drawing is a way to show three sides of a figure from a corner view. You can use isometric dot paper to make an isometric drawing. This paper has diagonal rows of dots that are equally spaced in a repeating triangular pattern. CONFIDENTIAL

  28. Drawing an isometric View of an Object Draw an isometric view of the given object. assume there are no hidden cubes. CONFIDENTIAL

  29. In a perspective drawing, nonvertical parallel lines are drawn so that they meet at a point called a vanishing point. Vanishing point are located on a horizontal line called the horizon. A one-point perspective drawing contains one vanishing points. A two-point perspective drawing contains two vanishing points. Vanishing point s Vanishing point one-point perspective two-point perspective CONFIDENTIAL

  30. Drawing an Object in Perspective 3 A) Draw a cube in one-point perspective. Draw a horizontal line to represent the horizon. Mark a vanishing point on the horizon. This is the front of the cube. From each corner of the square, lightly draw dashed segments to the vanishing point. Next page  CONFIDENTIAL

  31. Lightly draw a smaller square with vertices on the dashed segments. This is the back of the cube. Draw the edges of the cube, using dashed segments for hidden edges. Erase any segments that are not part of the cube. Next page  CONFIDENTIAL

  32. B) Draw a rectangular prism in two-point perspective. From each endpoint of the segment, lightly draw dashed segments to each vanishing point. Draw two vertical segments connecting the dashed lines. These are other vertical edges of the prism. Draw a horizontal line to represent the horizon. Mark two vanishing points on the horizon. Then draw a vertical segment below the horizon and between the vanishing points. This is the front edge of the prism. Next page  CONFIDENTIAL

  33. Lightly draw dashed segments from each endpoint of the two vertical segments to the vanishing points. Draw the edges of the prism, using dashed lines for hidden edges. Erase any lines that are not part of the prism. CONFIDENTIAL

  34. Relating Different Representations of an Object 4) Determine whether each drawing represents the given object. Assume there are no hidden cubes. B A No; the figure in the drawing is made up of four cubes, and the object is made up of only three cubes. Yes; the drawing is a one-point perspective view of the object. Next page  CONFIDENTIAL

  35. C D Top Back Right Left Front Bottom No; the cubes that share a face in the object do not share a face in the drawing. Yes; the drawing shows the six orthographic views of the object. CONFIDENTIAL

  36. You did a great job today! CONFIDENTIAL

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