Similarity 2
Golden Ratio
Name____________________________
Activity
American researcher, Jay Hambridge, established that indeed the Golden Ratio could be found not only in Greek
temples and sculpture, but also in the proportions of the human skeleton. The ratio of the total height to the
height of the navel is a close approximation to the Golden Ratio. Other writers and researchers have claimed
that ratios of many other parts of the human body are also in the Golden Ratio. In other words, we probably all
have some proportions close to the Greek ideal somewhere in our bodies.
Let’s see if the Golden Ratio is somewhere in each of us. Form groups of two and fill in the table with your
names. Use your ruler to measure each body part and make a ratio putting the longer length in the numerator.
Divide the numerator by the denominator to get a scale factor. Record your results.
Person’s Name
B/N
F/K
L/H
A/E
X/Y
Step 1: Measure the height (B) and the navel height (N) of each member of your group. Calculate the ratios B/N.
Record them in your table.
Step 2: Measure the length (F) of an index finger and the distance (K) from the finger tip to the big knuckle of
each member of your group. Calculate the ratios F/K. Record them in your table.
Step 3: Measure the length (L) of a leg and the distance (H) from the hip to the kneecap of everyone in your
group. Calculate and record the ratios L/H.
Step 4: Measure the length (A) of an arm and the distance (E) from the finger tips to the elbow of everyone in
your group. Calculate and record the ratios A/E.
Step 5: Select another pair of lengths (X and Y) on the body that you suspect may be in the golden ratio.
Measure these lengths. Calculate the ratios (large to small) and record them.
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Similarity 2
Similar Figures
Name ______________________________
Worksheet
6
5
, then 5x =
.

x
11
13
x -2
13
3. If
, then
=

x -2
10
7
6
5
x
 , then =
x
9
6
x
4. If 4x = 7y , then
=
y
1. If
2. If
.
5. If x : 10 = 7 : 11, then 11x =
7. In the proportion
the means.
.
.
x
9
4
 , then
=
2
4
2
.
4
9
 , ______ and ______ are the extremes and ______ and ______ are
5
7
8. Is the following a true proportion?
Find the value of x in each problem.
x
3
9
x = _______ 10.

6
5
12.
6. If
.
4
4
x = ______

x -1
11
13.
55
35

143
91
21 : 6 = 7 : x
x3
9

4
8
x = _______
x = _______
11.
4x
x -2

5
2
14.
x 1
x4
x = _____

5
8
x = _____
Solve the following problems.
15. A car travels 106 miles on 4 gallons of gas. How far can it be expected to travel on a full tank of 16
gallons?
16. A recipe for six dozen cookies calls for 2 ½ cups of flour. How many cups of flour are needed for
10 dozen cookies?
17. In a mixture of concrete, the ratio of cement to sand is one to four. How many shovels of cement
are needed to mix with 80 shovels of sand?
18. On a map, 1 in represents 100 miles. Find the actual distance between 2 towns that are 5 ¼ in. apart
on the map.
19. The ratio of two complementary angles is 7 : 11. Find the measure of each angle.
20. The ratio of angles in a triangle is 1 : 2: 6. Find the measure of each angle.
21. The ratio of two supplementary angles is 5 : 7. Find the measure of the smaller angle.
Find the ratio of x to y in each problem.
22.
25x = 35 y
x

y
.
23.
x - 3y
2

xy
3
x

y
.
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