# 13.3: Perspective Drawing

**At Grade**Created by: CK-12

*This activity is intended to supplement Geometry as an end-of-the-year activity.*

## Problem 1– One-point perspective

Open the *Cabri Jr*. file *RECPRISM*. Follow these steps to complete the drawing of a rectangular prism in one-point perspective.

- Use the
**Segment**tool to draw \begin{align*}\overline{AB}\end{align*}AB¯¯¯¯¯¯¯¯ and \begin{align*}\overline{AC}\end{align*}AC¯¯¯¯¯¯¯¯ . These two segments are called*vanishing segments*because they connect a point on the figure to the vanishing point. - Create \begin{align*}\overline{FG}\end{align*}
FG¯¯¯¯¯¯¯¯ such that \begin{align*}F\end{align*}F is between \begin{align*}A\end{align*}A and \begin{align*}B\end{align*}B , \begin{align*}G\end{align*}G is between \begin{align*}A\end{align*}A and \begin{align*}C\end{align*}C , and \begin{align*}\overline{FG}\|\overline{BC}\end{align*}FG¯¯¯¯¯¯¯¯∥BC¯¯¯¯¯¯¯¯ as shown in the diagram to the right.

To do this, you will need to use the **Point On, Parallel, Intersection, Hide/Show**, and **Segment** tools. Ask your teacher if you need help.

- Hide the vanishing segments, \begin{align*}\overline{AB}\end{align*}
AB¯¯¯¯¯¯¯¯ and \begin{align*}\overline{AC}\end{align*}AC¯¯¯¯¯¯¯¯ , and draw \begin{align*}\overline{BF}\end{align*}BF¯¯¯¯¯¯¯¯ and \begin{align*}\overline{CG}\end{align*}CG¯¯¯¯¯¯¯¯ . Then drag the vanishing point to the far left or far right. What do you notice? - Draw vanishing segments \begin{align*}\overline{AD}\end{align*}
AD¯¯¯¯¯¯¯¯ and \begin{align*}\overline{AE}\end{align*}AE¯¯¯¯¯¯¯¯ . Then use the**Perp**. tool construct two lines perpendicular to \begin{align*}\overline{FG}\end{align*}FG¯¯¯¯¯¯¯¯ —one through \begin{align*}F\end{align*}F and the other through \begin{align*}G\end{align*}. - Create \begin{align*}\overline{GH}\end{align*} and \begin{align*}\overline{FJ}\end{align*} using the
**Intersection, Hide/Show**, and**Segment**tools. - Hide the vanishing segments, and draw the three remaining edges of the rectangular prism.

Drag the vanishing point \begin{align*}(A)\end{align*} and edges, *not* the vertices, of the rectangular prism. When you finish exploring, you may use the **Hide/Show** or **Display** tool to hide or dash the “hidden lines.”

Then use similar steps to construct a triangular prism in one-point perspective using the *Cabri Jr*. file *TRIPRISM*.

## Problem 2 – Two-point perspective

Open the *Cabri Jr*. file *TWOPERSP*. Follow these instructions to construct a rectangular prism in two-point perspective.

- Draw four vanishing segments: \begin{align*}\overline{AC}\end{align*}, \begin{align*}\overline{AD}\end{align*}, \begin{align*}\overline{BC}\end{align*}, and \begin{align*}\overline{BD}\end{align*}.
- Use the
**Point On, Parallel, Intersection, Hide/Show**, and**Segment**tools as you did in

Problem 1 to construct two more vertical edges of the prism, \begin{align*}\overline{EF}\end{align*} and \begin{align*}\overline{GH}\end{align*}. Label them such that \begin{align*}\overline{CD}\end{align*} is the “middle” edge, with \begin{align*}\overline{EF}\end{align*} on its left and \begin{align*}\overline{GH}\end{align*} on its right.

- The three vertical segments represent the “side” edges of the left and right faces of the rectangular prism. Draw the four segments that represent the “top” and “bottom” edges of these faces.
- Hide the four vanishing segments, and then draw four more: from \begin{align*}E\end{align*} and \begin{align*}F\end{align*} to \begin{align*}B\end{align*} and from \begin{align*}G\end{align*} and \begin{align*}H\end{align*} to \begin{align*}A\end{align*}. Mark the intersection of the upper two vanishing segments \begin{align*}J\end{align*} and that of the lower two vanishing segments \begin{align*}K\end{align*}, and draw \begin{align*}\overline{JK}\end{align*}.
- Hide the vanishing segments, and then draw the remaining four edges of the prism.

Drag the vanishing points and edges or vertices of the rectangular prism. When you finish exploring, you may again use the **Hide/Show** or **Display** tool to hide or dash the “hidden lines.”

In the space below, describe the similarities and differences between drawing in one-point perspective and drawing in two-point perspective. Then advance to Problem 3.

## Problem 3 – An isometric drawing

Open the *Cabri Jr*. file *ISODRAW*. Construct an isometric drawing of a rectangular prism by following these steps.

- First, you will construct lines using the
**Parallel**tool. Refer to the diagram to the right.

You should construct two lines though point \begin{align*}D\end{align*} (one parallel to \begin{align*}\overline{AB}\end{align*}, the other to \begin{align*}\overline{BC}\end{align*}) and two lines that are parallel to \begin{align*}\overline{BD}\end{align*} (one through point \begin{align*}A\end{align*}, the other through point \begin{align*}C\end{align*}).

- Use the
**Intersection**tool to mark the lower left intersection as point \begin{align*}E\end{align*} and the lower right intersection as point \begin{align*}F\end{align*}. - Hide the parallel lines, and use the
**Segment**tool to draw \begin{align*}\overline{AE}\end{align*}, \begin{align*}\overline{CF}\end{align*} \begin{align*}\overline{DE}\end{align*}, and \begin{align*}\overline{DF}\end{align*}. - Using the same sequence of tools, construct the remaining edges: \begin{align*}\overline{AG}\end{align*}, \begin{align*}\overline{CG}\end{align*}, \begin{align*}\overline{EH}\end{align*}, \begin{align*}\overline{FH}\end{align*}, and \begin{align*}\overline{GH}\end{align*}. (Can you figure out how?)

Grab and drag points \begin{align*}A\end{align*}, \begin{align*}C\end{align*}, or \begin{align*}D\end{align*} to change the dimensions of the rectangular prism. Again, you may change the appearance of the “hidden lines.”

In the space below, describe any similarities and differences between an isometric drawing and a perspective drawing.