1. 7.2 Properties of Proportions P.O.P.’s
Geometry
7.2 Properties of Proportions
P.O.P.’s

2. Introduction Extreme Mean Mean Extreme
The first and last terms of a proportion are the extremes.
(think: extreme weather)
The second and third terms of a proportion are the means.
(think: the mean = average is in the middle)

3. P.O.P.’s (there are 5 P.O.P.’s)
The product of the means equals the product of the extremes.
Given:
Is equivalent to:
ad = bc
Example:
Is equivalent to:
1(80) = 20(4)
80 = 80

4. P.O.P.
Switching the means(or extremes) results in an equivalent proportion.
Given:
Is equivalent to:
A method to check: See if the
mean x mean = extreme x extreme
Is equivalent to the given.
&
ad = bc
ad = bc
ad = bc
Example:
Is equivalent to:
&
30 = 30
30 = 30

5. P.O.P.
Inverting the entire proportion results in an equivalent proportion.
Given:
Is equivalent to:
Does it check?
ad = bc
ad = bc
Example:
Is equivalent to:
54 = 54

6. P.O.P. Adding the denominator on each side to the numerator above it
results in an equivalent proportion.
Given:
Is equivalent to:
Does it check?
ad = bc
d(a + b) = b(c + d)?
da + db = bc + bd?
da = bc
Example:
Is equivalent to:
140 = 140

7. P.O.P. In an extended proportion, the ratio of
sum of all numerators: sum of all denominators
is equivalent to each individual given ratio.
Given:
Are all equivalent to:
Example:
Are all equivalent to:

8. Which proportions are equivalent to ?
Yes!
Yes!
Yes!
No!

9. A Few Together from the HW
P. 247 #27 P. 248 #35

10. HW
P CE(1-15 Odd) WE(1-39 Odd)

11. Page 246 CE (1-9, 11, 13, 14) 1)
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