1. Pre-Algebra 6-5 Drawing Three-Dimensional Figures Page 298 ANSWERS Refer to the answer key

2. Our learning goal is to be able to solve for perimeter, area and volume. Learning Goal Assignments 1.Perimeter and Area of Rectangles and Parallelograms 2.Perimeter and Area of Triangles and Trapezoids 3.The Pythagorean Theorem 4.Circles 5.Drawing Three-Dimensional figures 6.Volume of Prisms and Cylinders 7.Volume of Pyramids and Cones 8.Surface Area of Prisms and Cylinders 9.Surface Area of Pyramids and Cones 10.Spheres

3. Pre-Algebra 6-5 Drawing Three-Dimensional Figures Learning Goal Assignment Learn to draw and identify the parts of three-dimensional figures.

4. Pre-Algebra 6-5 Drawing Three-Dimensional Figures Pre-Algebra HOMEWORK Page 305 7-23 ODD!

5. Pre-Algebra 6-5 Drawing Three-Dimensional Figures 6-5 Drawing Three-Dimensional Figures Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

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

8. Pre-Algebra 6-5 Drawing Three-Dimensional Figures Learning Goal Assignment Learn to draw and identify the parts of three-dimensional figures.

9. Pre-Algebra 6-5 Drawing Three-Dimensional Figures face edge vertex perspective vanishing point horizon line Vocabulary

10. Pre-Algebra 6-5 Drawing Three-Dimensional Figures 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.

11. Pre-Algebra 6-5 Drawing Three-Dimensional Figures Edge Face Isometric dot paper can be used to draw three-dimensional figures. Vertex

12. Pre-Algebra 6-5 Drawing Three-Dimensional Figures Use isometric dot paper to sketch a rectangular box that is 5 units long, 3 units deep and 2 units tall. Additional Example 1: Drawing a Rectangular Box 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.

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

14. Pre-Algebra 6-5 Drawing Three-Dimensional Figures 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.

15. Pre-Algebra 6-5 Drawing Three-Dimensional Figures 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

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

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

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

19. Pre-Algebra 6-5 Drawing Three-Dimensional Figures 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.

20. Pre-Algebra 6-5 Drawing Three-Dimensional Figures Additional Example 2: Sketching a One Point Perspective Drawing Sketch a one-point perspective drawing of a cube. V A B C D G 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 3: Choose a point G on BV and draw a smaller square that has G as one of its vertices. 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.

21. Pre-Algebra 6-5 Drawing Three-Dimensional Figures Additional Example 2: Sketching a One Point Perspective Drawing 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 3: Choose a point G on BV and draw a smaller square that has G as one of its vertices. 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. Sketch a one-point perspective drawing of a cube.

22. Pre-Algebra 6-5 Drawing Three-Dimensional Figures Try This: Example 2 V A B C D G Step 2: Mark a vanishing point V above your rectangle, and draw a dashed line from each vertex to V. 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 3: Choose a point G on BV and draw a smaller rectangle that has G as one of its vertices. 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.

23. Pre-Algebra 6-5 Drawing Three-Dimensional Figures A B C D G Try This: Example 2 Step 2: Mark a vanishing point V above your rectangle, and draw a dashed line from each vertex to V. Step 1: Draw a rectangle. This will be the front face. Label the vertices A through D. Step 3: Choose a point G on BV and draw a smaller rectangle that has G as one of its vertices. 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. Sketch a one-point perspective drawing of a rectangular box.

24. Pre-Algebra 6-5 Drawing Three-Dimensional Figures 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.

25. Pre-Algebra 6-5 Drawing Three-Dimensional Figures Additional Example 3: Sketching a Two-Point Perspective Drawing Sketch a two-point perspective drawing of a cube. 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.

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

27. Pre-Algebra 6-5 Drawing Three-Dimensional Figures Try This: Example 3 A D V W C E Darken the visible edges. Erase the horizon and dashed segments. 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. Sketch a two-point perspective drawing of a rectangular box. Label C on DV and E on DW so that CE = ED. Draw vertical segments through C and E. Draw EV and CW.

28. Pre-Algebra 6-5 Drawing Three-Dimensional Figures 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. 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. Sketch a two-point perspective drawing of a rectangular box. Try This: Example 3

29. Pre-Algebra 6-5 Drawing Three-Dimensional Figures 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.