7th Grade Math

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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

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