7th Grade Math

(Marvins-Underground-K-12) #1
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Similarity and Proportional Reasoning


PART A B C


Multi-Part
Lesson 3

GLE 0706.2.3
Develop an understanding of
and apply proportionality.
Also addresses GLE 0706.1.3,
GLE 0706.1.7, SPI 0706.2.7.

The Golden Rectangle


Cut out a rectangle length

width

34
21

21
13
ratio
decimal

that measures 34 units
by 21 units. Find the
ratio of the length to
the width. Express it as
a decimal to the
nearest hundredth. Record your data in a table.

Cut this rectangle into two

Rectangle Square

parts. One part is the largest
possible square, and the
other part is a rectangle.
Record the rectangle’s length
and width. Write the ratio of
length to width. Express it as a decimal to the nearest
hundredth and record in the table.

Repeat the procedure described in Step 2 until the
remaining rectangle measures 3 units by 5 units.

the Results



  1. Describe the pattern in the ratios you recorded.

  2. MAKE A CONJECTURE If the rectangles you cut out are described as
    golden rectangles, what is the value of the golden ratio?

  3. Write a definition for a golden rectangle. Use the word ratio in
    your definition. Then describe the shape of a golden rectangle.

  4. Determine whether all golden rectangles are similar. Explain.

  5. MATH IN THE MEDIA There are
    many examples of the golden
    rectangle in architecture. One
    is shown at the right. Use the
    Internet or another resource
    to find three places where the
    golden rectangle is used in
    architecture.


Main Idea
Find the value of the
golden ratio.

Lesson 3C Similarity and Proportional Reasoning 303

293_303_C05_L3_895130.indd 303 12/29/09 1:10 PM

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