Similar figures have the same shape but not necessarily the same size. You can also generate similar figures, including 3-dimensional figures, using a scale factor.

Consider the two prisms shown below.

Two prisms with dimensions labeled

These prisms are both right rectangular prisms, so the angles formed by the edges and faces at each vertex are all right angles. However, the sides are not congruent. Let’s take a closer look at the corresponding edge lengths using proportions.


8.5 centimeters over 4.25 centimeters 4.8 centimeters 2.4 centimeters = 2       6.5 centimeters over 3.25 centimeters 2.2 centimeters 1.1 centimeters = 2       6.5 centimeters over 3.25 centimeters 16 centimeters 8 centimeters = 2

Since the ratios of the corresponding side lengths are proportional, we can say that the prisms are similar.

We can also use the ratios of corresponding edge lengths to identify the scale factor that is used to generate Prism 2 from Prism 1.

Two rectangles with dimensions and scale factor labeled

In this example, the scale factor is 2 because the dimensions of Prism 1 are multiplied by 2 to generate the dimensions of Prism 2.

How does this dilation affect the volume of the new prism? You will investigate that relationship.