Warm Up 1. Determine if the statement is true or false. If then
2. Find the geometric mean of 8 and 20. 3. Solve the following proportions: a) b)
*Hint: You will have to factor*
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HW Answers - Worksheet 8.2 B
5. true 15. 6. false 16. 7. true 17. 8. false 18. 9. √60 = 2√15 10. √96 = 4√6 11. √120 = 2√30 12. √150 = 5√6 13. √192 = 8√3 14. √480 = 4√30
24/7 48/5 $47.27 $20.40
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8.3 Similar Polygons EQ: What are similar polygons and how do we use them? Similar Polygons - when there is a correspondence between two polygons such that their corresponding angles are congruent and the lengths of corresponding sides are proportional. (same shape - different size)
C
G
F
B
E
means similar corresponding vertices listed in order just like with congruence statements
H
A
D
Statement of Proportionality
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Examples: 1. Trapezoid ABCD is similar to trapezoid PQRS. List all the pairs of congruent angles and write the statement of proportionality.
A
B
Q
R S
P
D
C
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Determine whether the polygons are similar. If so, write a similarity statement. 2.
K 9 E 15 R 6 10
J
12
W
8
M
3.
A
6
C 10
H 4
F
8
D
B
E
G
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SCALE FACTOR - If two polygons are similar, then the ratio of two corresponding sides is called the scale factor. K 9 E 15 R 6 10
J
12
W
8
M
The scale factor of The scale factor of
KEW to RJM to
RJM is 3/2. KEW is 2/3.
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The rectangular patio around a pool is similar to the pool. First, find the value of x. Then calculate the scale factor of the patio to the pool, and find the ratio of their perimeters.
x
40 ft 65 ft
39 ft
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Theorem 8.1 If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.
Q
P
K
L
S
R
N
M
If PQRS~KLMN, then
scale factor
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1. Polygon ABCD ~ Polygon GHIJ.
a. Find the scale factor of polygon ABCD to polygon GHIJ. b. Find the scale factor of polygon GHIJ to polygon ABCD. c. Find the values of x and y. d. Find the perimeter of each polygon. e. Find the ratio of the perimeter of ABCD to the perimeter of GHIJ.
A 11 D
8
B 11
5.5
C x y G H
8
J
I
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2. The ratio of one side of ABC to the corresponding side of similar DEF is 5:8. The perimeter of DEF is 96 inches. What is the perimeter of ABC?
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HW - pg. 476 # 9 -42 mult. of 3, 46, 47
Quiz Sections 8.1 - 8.3
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