1. Rectangle Ratios What does the word “similar” mean to most people?
Name: ______________________________________
Rectangle Ratios
What does the word “similar” mean to most people?
What is the mathematical meaning of “similar”?
Describe some ways we can prove that rectangles are similar.

2. 4. With a partner cut the two pages of rectangles out on the bold lines.
Sort the 14 rectangles into 3 “families”.
Explain why you sorted them as you did.

3. Describe the relationships that can be seen within the families.
Stack the families with the smallest on top, so that one corner and one edge are on top of one another.
What observations can now be made of the families?

4. Using another sheet of paper, cut out another rectangle that would fit into one of the “families”, other than the family of squares.
10. Using the Rectangle Ratios charts, record by “family” the length and width of the rectangles.

5. Describe any numeric pattern you can see in the charts.
The “scale factor” is a constant ratio of one measurement to another. Write a scale factor of the width to the length for each “family”.
Square family __________
Long family __________
Not-so-long family __________

6. 13. Make a graph for the LONG rectangle “family”, using the data from your chart. Plot the points (length, width).
14. Connect the points and describe what it looks like.
15. List three other points that would be on your line. What would these points mean?

7. 16. How far UP and how far OVER would you have to move from one point to another?
Write this as a ratio of UP to OVER.
If you do this for all the points on the graph would the ratios equal? Explain.

8. For this graph the up and down axis (y axis) is the ____________ and the left and right axis (x axis) is the _____________.
The UP:OVER ratio could also be called the width:length ratio. Sometimes that’s called the “rate of change”. Compare the “rate of change” to the scale factor you wrote for this family in question 12.
Using this scale factor write a rule to find any size rectangle in this family.