One common situation that can be represented with proportional relationships is analyzing similar figures. Similar figures are different sizes of the exact same shape.
When setting up a proportion for a pair of similar figures, you can only compare the lengths of corresponding sides. Corresponding sides are the matching sides of the similar figures. In the picture above, the corresponding sides are labeled with upper and lower case of the same letter.
Select the matching pairs by clicking on the tile that represents one of the corresponding sides or one of the equivalent ratios:
 Corresponding sides
 Equivalent ratios
One example of using similar figures is making scale drawings or models.
Read the following, and answer the questions below.
An architect is drawing a scale picture of a house. The dimensions of the actual rooms and the rooms in the picture are listed in the table below.
Copy the table into your notes, and fill in the missing information.
Actual Measurement 
Process  Picture Measurement 


Living Room 
Length 
20 Feet 
20 ( $\frac{1}{4}$) = 5 
5 inches 
Width 
12 Feet 
12 ( $\frac{1}{4}$ ) = 3 
3 inches 

Dining Room 
Length 
18 Feet 
4.5 inches 

Width 
10 Feet 

Kitchen 
Length 
12 Feet 

Width 
16 Feet 

Bedroom 
Length 
12 Feet 

Width 
10 Feet 
Click here to see the completed table.
 What do you notice is constant in the table?
 What proportional relationship could you use to relate p, a measurement in the picture, with a, an actual measurement?
 Given that y → picture measurement, k → $\frac{1}{4}$ and x → actual measurement use the variables ‘p’ and ‘a’ to rewrite the proportional relationship as an equation that looks like y = kx.
 If the architect were to measure one of the bathrooms in the house to be 10 feet long by 8 feet wide, what would the dimensions of the bathroom be in the picture?
 If the architect were to measure the length of a second bedroom in the house to be 15 feet long, what would the width of the second bedroom be in the picture?