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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