Concept Byte: Perspective Drawing

Use With Lesson 11-1

EXTENSION

You can draw a three-dimensional space figure using a two-dimensional perspective drawing. Suppose two lines are parallel in three dimensions, but extend away from the viewer. You draw them—and create perspective—so that they meet at a vanishing point on a horizon line.

Example 1

Draw a cube in one-point perspective.

  • Step 1

    Draw a square. Then draw a horizon line and a vanishing point on the line.

    A square has a horizontal line above with a point on the line centered above the square.

  • Step 2

    Lightly draw segments from the vertices of the square to the vanishing point.

    The square has lines extending from each vertex to the point on the horizontal line above.

  • Step 3

    Draw a square for the back of the cube. Each vertex should lie on a segment you drew in Step 2.

    The square has a smaller square drawn with vertices on the lines leading from the vertices of the large square to the point on the line.

  • Step 4

    Complete the figure by using dashes for the hidden edges of the cube. Erase unneeded lines.

    Lines connecting the vertices of the two squares form a cube, with edges of the front and top faces solid.

Example 2

Draw a box in two-point perspective.

  • Step 1

    Draw a vertical segment. Then draw a horizon line and two vanishing points on the line.

    A vertical line segment is drawn below a horizontal line, which has points at each end, equal distances from the vertical line.

  • Step 2

    Lightly draw segments from the endpoints of the vertical segment to each vanishing point.

    Two lines extend from each end of the vertical line to the points on the horizontal line.

  • Step 3

    Draw two vertical segments between the segments of Step 2.

    Two vertical lines are drawn between the lines leading to each point, on either side of the original vertical line.

  • Step 4

    Draw segments from the endpoints of the segments you drew in Step 3 to the vanishing points.

    The two vertical lines have lines extending from either end to the point on the line on the opposite side of the original vertical line.

  • Step 5

    Complete the figure by using dashes for the hidden edges of the figure. Erase unneeded lines.

    The intersections of the previous four lines form vertices of a cube, with edges of the top, front, and left faces solid.


End ofPage 696

Table of Contents

Prentice Hall Geometry Chapter 1 Tools of Geometry Chapter 2 Reasoning and Proof Chapter 3 Parallel and Perpendicular Lines Chapter 4 Congruent Triangles Chapter 5 Relationships Within Triangles Chapter 6 Polygons and Quadrilaterals Chapter 7 Similarity Chapter 8 Right Triangles and Trigonometry Chapter 9 Transformations Chapter 10 Area Chapter 11 Surface Area and Volume Chapter 12 Circles Skills Handbook Reference Visual Glossary Selected Answers Index Acknowledgments