7-2 Similar Polygons
Similar Figures
 Figures that have the same shape but are not necessarily the same size are similar.
 The symbol for similar is ______
 Two polygons are similar if:
1. Corresponding angles are congruent
2. Corresponding sides are proportional
 The ratio of the lengths of corresponding sides is the ________________________.
Similar Figures Practice 1:
 Are the triangles similar? How do you know you are correct?
Similar Figures Practice 2:
 LMNO ~ QRST
 Find x.

Are the figures similar? How do you know you are
correct?
Exploring Special Similar Figures
 You will work through a series of activities using your iPad. Follow the sequence on your
instruction sheet, and consider the special case of Fibonacci numbers and the Golden
Rectangle
Tasks:
1. Follow the link from Edmodo to the Fibonacci numbers & Golden Rectangle Online Lesson.
2. Using your iPad, work through the activities on the first page:
a. Record the Fibonacci sequence in the first column of a new spreadsheet in Numbers.
𝐹[𝑛]
b. Record the ratios found by 𝐹[𝑛−1] in the second column in your spreadsheet. Use a formula (see
picture) to do the calculations.
Formula
c. Graph the ratios with the Fibonacci
sequence as the x axis and the ratios as the
y axis.
d. Describe the graph. What is happening to
𝐹[𝑛]
𝐹[𝑛−1]
as the Fibonacci number increases?
3. Continue to the next page by following the link at the bottom of the page.
4. Use GeoGebra to construct the series of squares as indicated in the directions on the page. Use the
segment between two points tool for the construction.
5. What do you notice about the ratio between the length and width of each rectangle you’ve created in
the pattern?
6. Use the Circular Arc with Center Between Two Points tool
(you will need to get it from the Circle
and Arc Tools menu) to create the arcs as directed on the page. To do the arcs, you will need to click on
one point to set the center, and then two other points to tell the computer which points it should go
between. To enable you to complete this step properly, look at this example: I clicked on point G to set
the radius of the circle equal to the length of one side of the square, and then clicked on points N and
then K to create the arc.
7. Describe the pattern you’ve created.
8. Click on the “Golden Ratio” link at the bottom of the page to go to the next lesson.
9. Follow the directions to take measures of various rectangles as instructed. Create and complete your
table in a new page in your Numbers doc.
10. What do you notice about the ratios you’ve found?
11. Click on the link at the bottom of the page to go on to the next page and read about this ratio.
WRAP UP QUESTIONS:
How is the Fibonacci sequence related to the ratio we found with the rectangles we drew?
Why do you think we’re doing this stuff with the similar figures unit?