# Similar Rectangles

Use a ruler and cut paper rectangles with the following dimensions (all dimensions are in inches):

A) 3 by 5

B) 4 by 6

C) 6 by 8

D) 5 by 7

E) 8.5 by 11

F) 5.5 by 8.5

G) 4.25 by 5.5

- Sort the rectangles by shape.

- Make a list of pairs of rectangles that appear to be scaled versions of each other (or have sides that are proportional).

Two rectangles are **similar **if they are the exact same shape but are dissimilar in size. Also, to be similar, the rectangles must have side lengths that are proportional.

**Example 1**: The following two rectangles are similar.

The sides lengths can be compared multiplicatively:

- The longer dimension of each rectangle is twice the measure of the shorter dimension.
- When corresponding side lengths are compared, the larger rectangle’s dimensions are 1.6 times as long as the smaller rectangle’s.

**Example 2**: The following two rectangles are not similar.

The ratios of the sides of the rectangles are not the same meaning that the sides are not proportional.

- The ratio of the sides of the first rectangle is 2/3.
- The ratio of the sides of the second rectangle is 3/4.

3. Use ratios of the sides to determine which pairs of rectangles are similar. How did your list compare?

A) 3 by 5

B) 4 by 6

C) 6 by 8

D) 5 by 7

E) 8.5 by 11

F) 5.5 by 8.5

G) 4.25 by 5.5

*Note: Increasing one dimension, while keeping the other the same, is not scaling, and therefore, not a multiplicative comparison. And, increasing each dimension by the same length is not scaling.