# Representing Solids

## Big Picture

There are four main ways to visualize a three-dimensional figure in two dimensions: isometric view, orthographic view, cross-sectional view, and a net.

## Key Terms

Perspective: Artistic illusion used to make things in the distance look smaller by using a vanishing point where parallel lines converge.

Isometric View: Three-dimensional view of a solid that does not typically include perspective.

Orthographic Projection: A view that shows a flat representation of each side of the figure’s sides.

Cross Section View: A slice of a three-dimensional figure.

Net: A two-dimensional figure that can be folded into a geometric solid.

## Isometric View

The  perspective view looks more “real” to the eye, but isometric view is more useful for measuring and comparing distances. It is often shown in a transparent form; shading and coloring can also be applied to make the figure look more realistic.

## Orthographic View

How to show a figure in an orthographic projection:

• Place it in an imaginary box.
• Project each side of the figure out to each of the walls of the box.
• The image of the side will be on each of the six walls of the box.

For example:

# Representing Solids Cont.

## Cross Section View

This is similar to slicing a 3-dimensional figure into a series of thin slices. Each slice will show a cross section view. Depending on the angle at which we slice the figure, there are many possible cross sections that we can get.

## Net

Nets are just another way to model a figure. If a net is cut out, it can be folded into a model of a figure. A single figure can have multiple possible nets.