1. Geom8­1Part2.notebook January 18, 2012
Good morning!
When the bell rings, I would like everyone to be in their seats
working on the bell work. Thank you!
BELL WORK:
The ratio of the measures of the sides of a quadrilateral is 2:3:5:7.
If the figure's perimeter is 68, find the length of each side.
Homework questions: p.329
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2. Geom8­1Part2.notebook January 18, 2012
Warm­up Example: Find the 4th term of a proportion if the
first 3 terms are 2, 3, and 4.
Parts of a ratio:
Theorem: In a proportion, the product of the means is equal to the
product of the extremes. (Means­Extremes Products Theorem)
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3. Geom8­1Part2.notebook January 18, 2012
Theorem: In a product of a pair of nonzero numbers is equal to the
product of another pair of nonzero numbers, either pair of numbers
may be made the extremes and the other pair means.
(Means­Extremes Ratio Theorem)
Example: If x(a + b) = y(c + d), find the ratio of x to y.
If 3x = 4y, find the ratio of x to y.
Mean Proportion (means are the same):
When this happens, x is called the geometric mean
(or mean proportional) between the extremes.
Example: Find the geometric mean between 4 and 16.
Example: If 4 is a geometric mean between 6 and a number,
what is the number?
What is the geometric mean between 1 and 9?
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4. Geom8­1Part2.notebook January 18, 2012
The arithmetic mean is the average of two numbers.
Find the arithmetic mean of 52 and 68.
Last example: Is x a equivalent to x ­ 2y a ­ 2b ?
=
y = b y b
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5. Geom8­1Part2.notebook January 18, 2012
EXIT SLIP: Find the positive geometric and arithmetic means
between each pair of numbers. Tell me which mean is
greater in each case.
a) 8 and 50
b) 6 and 12
Homework: p.329 #1b, 6,11
due Friday
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