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Pre-Algebra
6-5 Drawing Three-Dimensional Figures
6-5 Drawing Three-Dimensional Figures
Pre-Algebra
Warm Up
Problem of the Day
Lesson Presentation
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
196ft2; 615.4 ft2
5m; 15.7 m
8.8cm; 27.6 cm
49ft2; 153.9 ft2
Pre-Algebra
6-5 Drawing Three-Dimensional Figures
Problem of the DayWhat is the least number of lines needed to draw 5 squares ?
6
Pre-Algebra
6-5 Drawing Three-Dimensional Figures
Learn to draw and identify the parts of three-dimensional figures.
Pre-Algebra
6-5 Drawing Three-Dimensional Figures
face
edge
vertex
perspective
vanishing point
horizon line
Vocabulary
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.
Pre-Algebra
6-5 Drawing Three-Dimensional Figures
Edge
Face
Isometric dot paper can be used to draw three-dimensional figures.
Vertex
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.
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
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.
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Pre-Algebra
6-5 Drawing Three-Dimensional Figures
Try This: Example 1 Continued
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Step 1: Lightly draw the edges of the bottom face. It will look like a parallelogram. 2 units by 4 units
Pre-Algebra
6-5 Drawing Three-Dimensional Figures
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Step 2: Lightly draw the vertical line segments from the vertices of the base. 3 units high
Try This: Example 1 Continued
Pre-Algebra
6-5 Drawing Three-Dimensional Figures
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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
Pre-Algebra
6-5 Drawing Three-Dimensional Figures
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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
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.
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
AB
CD
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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