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6-5

6-5. Drawing Three-Dimensional Figures. Warm Up. Problem of the Day. Lesson Presentation. Course 3. 6-5. Drawing Three-Dimensional Figures. Course 3. Warm Up. Find the circumference of each circle, both in terms of p and to the nearest tenth. Use 3.14 for p . 5 p m; 15.7 m.

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6-5

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  1. 6-5 Drawing Three-Dimensional Figures Warm Up Problem of the Day Lesson Presentation Course 3

  2. 6-5 Drawing Three-Dimensional Figures Course 3 Warm Up Find the circumference of each circle, both in terms of p and to the nearest tenth. Use 3.14 for p. 5p m; 15.7 m 1. radius 2.5 m 2. diameter 8.8 cm 8.8p cm; 27.6 cm Find the area of each circle, both in terms of p and to the nearest tenth. Use 3.14 for p. 3. radius 14 ft 196p ft2; 615.4 ft2 49p ft2; 153.9 ft2 4. diameter 14 ft

  3. 6-5 Drawing Three-Dimensional Figures Course 3 Problem of the Day What is the least number of lines needed to draw 5 squares ? 6

  4. 6-5 Drawing Three-Dimensional Figures Course 3 Drawing 3 Dimensional Figures Learn to draw and identify the parts of three-dimensional figures. Course 3

  5. 6-5 Drawing Three-Dimensional Figures Course 3 Vocabulary face edge vertex perspective vanishing point horizon line

  6. 6-5 Drawing Three-Dimensional Figures Course 3 Three-dimensional figures have faces, edges, and vertices. A face is a flat surface, an edge is where two faces meet, and a vertex is where three or more edges meet.

  7. 6-5 Drawing Three-Dimensional Figures Vertex Edge Face Course 3 Isometric dot paper can be used to draw three-dimensional figures.

  8. 6-5 Drawing Three-Dimensional Figures Course 3 Additional Example 1: Drawing a Rectangular Box Use isometric dot paper to sketch a rectangular box that is 5 units long, 3 units deep and 2 units tall. Step 1: Lightly draw the edges of the bottom face. It will look like a parallelogram. 3 units by 5 units Step 2: Lightly draw the vertical line segments from the vertices of the base. 2 units high Step 3: Lightly draw the top face by connecting the vertical lines to form a parallelogram. 3 units by 5 units Step 4: Darken the lines. Use solid lines for the edges that are visible and dashed lines for the edges that are hidden.

  9. 6-5 Drawing Three-Dimensional Figures Course 3 Additional Example 1: Continued Use isometric dot paper to sketch a rectangular box that is 5 units long, 3 units deep and 2 units tall.

  10. 6-5 Drawing Three-Dimensional Figures • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Course 3 Try This: Example 1 Use isometric dot paper to sketch a rectangular box that is 4 units long, 2 units deep, and 3 units tall.

  11. 6-5 Drawing Three-Dimensional Figures Course 3 Try This: Example 1 Continued Step 1: Lightly draw the edges of the bottom face. It will look like a parallelogram. 2 units by 4 units • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

  12. 6-5 Drawing Three-Dimensional Figures Course 3 Try This: Example 1 Continued Step 2: Lightly draw the vertical line segments from the vertices of the base. 3 units high • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

  13. 6-5 Drawing Three-Dimensional Figures Course 3 Try This: Example 1 Continued Step 3: Lightly draw the top face by connecting the vertical lines to form a parallelogram. 2 units by 4 units • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

  14. 6-5 Drawing Three-Dimensional Figures Course 3 Try This: Example 1 Continued Step 4: Darken the lines. Use solid lines for the edges that are visible and dashed lines for the edges that are hidden. • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

  15. 6-5 Drawing Three-Dimensional Figures Course 3 Perspective is a technique used to make drawings of three-dimensional objects appear to have depth and distance. In one-point perspective drawings, there is one vanishing point.

  16. 6-5 Drawing Three-Dimensional Figures V G A B Step 3: Choose a point G on BV and draw a smaller square that has G as one of its vertices. C D Course 3 Additional Example 2: Sketching a One Point Perspective Drawing Sketch a one-point perspective drawing of a cube. Step 1: Draw a square. This will be the front face. Label the vertices A through D. Step 2: Mark a vanishing point V above your square, and draw a dashed line from each vertex to V. Step 4: Darken the visible edges, and draw dashed segments for the hidden edges. Erase the vanishing point and the lines connecting it to the vertices.

  17. 6-5 Drawing Three-Dimensional Figures Step 3: Choose a point G on BV and draw a smaller square that has G as one of its vertices. Course 3 Additional Example 2: Sketching a One Point Perspective Drawing Sketch a one-point perspective drawing of a cube. Step 1: Draw a square. This will be the front face. Label the vertices A through D. Step 2: Mark a vanishing point V above your square, and draw a dashed line from each vertex to V. Step 4: Darken the visible edges, and draw dashed segments for the hidden edges. Erase the vanishing point and the lines connecting it to the vertices.

  18. 6-5 Drawing Three-Dimensional Figures V G A B Step 3: Choose a point G on BV and draw a smaller rectangle that has G as one of its vertices. C D Course 3 Try This: Example 2 Sketch a one-point perspective drawing of a rectangular box. Step 1: Draw a rectangle. This will be the front face. Label the vertices A through D. Step 2: Mark a vanishing point V above your rectangle, and draw a dashed line from each vertex to V. Step 4: Darken the visible edges, and draw dashed segments for the hidden edges. Erase the vanishing point and the lines connecting it to the vertices.

  19. 6-5 Drawing Three-Dimensional Figures G A B Step 3: Choose a point G on BV and draw a smaller rectangle that has G as one of its vertices. C D Course 3 Try This: Example 2 Sketch a one-point perspective drawing of a rectangular box. Step 1: Draw a rectangle. This will be the front face. Label the vertices A through D. Step 2: Mark a vanishing point V above your rectangle, and draw a dashed line from each vertex to V. Step 4: Darken the visible edges, and draw dashed segments for the hidden edges. Erase the vanishing point and the lines connecting it to the vertices.

  20. 6-5 Drawing Three-Dimensional Figures Course 3 You can also draw a figure in two-point perspective by using two vanishing points and a horizon line. Moving the horizon line up and down gives you different views of the figure.

  21. 6-5 Drawing Three-Dimensional Figures Draw a vertical segment AD. Draw a horizontal line above AD and label the vanishing points V and W. Draw dashed segments AV, AW, DV, and DW. Label C on DV and E on DW so that CE = ED. Draw vertical segments through C and E. Draw EV and CW. Course 3 Additional Example 3: Sketching a Two-Point Perspective Drawing Sketch a two-point perspective drawing of a cube.

  22. 6-5 Drawing Three-Dimensional Figures Course 3 Additional Example 3: Sketching a Two-Point Perspective Drawing Sketch a two-point perspective drawing of a cube. Darken the visible edges. Erase the horizon and dashed segments.

  23. 6-5 Drawing Three-Dimensional Figures V W E C D A Draw a vertical segment AD. Draw a horizontal line above AD and label the vanishing points V and W. Draw dashed segments AV, AW, DV, and DW. Label C on DV and E on DW so that CE = ED. Draw vertical segments through C and E. Draw EV and CW. Course 3 Try This: Example 3 Sketch a two-point perspective drawing of a rectangular box. Darken the visible edges. Erase the horizon and dashed segments.

  24. 6-5 Drawing Three-Dimensional Figures Draw a vertical segment AD. Draw a horizontal line above AD and label the vanishing points V and W. Draw dashed segments AV, AW, DV, and DW. Course 3 Try This: Example 3 Sketch a two-point perspective drawing of a rectangular box. Label C on DV and E on DW. Draw vertical segments through C and E. Draw EV and CW. Darken the visible edges. Erase the horizon and dashed segments.

  25. 6-5 Drawing Three-Dimensional Figures Course 3 Lesson Quiz 1. Use isometric dot paper to sketch a rectangle box 3 units tall with a base of 2 units by 5 units. 2. Sketch a cube in one-point perspective. 3. Sketch a brick in two-point perspective.

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