SIMILAR TEST REVIEW
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Transcript of SIMILAR TEST REVIEW
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SIMILAR TEST REVIEW
STUDY, STUDY, STUDY!!!
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HOW CAN A RATIO BE WRITTEN?
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HOW CAN A RATIO BE WRITTEN?
a : b
and
a/b
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HOW CAN A RATIO BE WRITTEN?
a : b
and
a/b
READS: A TO B
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What is the definition of aPROPORTION?
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What is the definition of aPROPORTION?
is an equation showing that two ratios are
EQUALto each other.
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WHAT PROPERTIES AND THEOREMS ARE USED FOR PROVING SIMILAR TRIANGLES?
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WHAT PROPERTIES AND THEOREMS ARE USED FOR PROVING SIMILAR TRIANGLES?
AASSSSAS
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SOLVING PROPORTIONS
1. 2.
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SOLVING PROPORTIONS
1. 2.
10(4) = 8(k) CROSS-MULTIPLY 1(99) = 9(X – 9)
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SOLVING PROPORTIONS
1. 2.
10(4) = 8(k) CROSS-MULTIPLY 1(99) = 9(X – 9)
40 = 8K MULTIPLY TERMS 99 = 9X - 81
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SOLVING PROPORTIONS
1. 2.
10(4) = 8(k) CROSS-MULTIPLY 1(99) = 9(X – 9)
40 = 8K MULTIPLY TERMS 99 = 9X - 81
SOLVE FOR X
5 = K 180 = 9X
20 = X
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SETTING UP PROPORTIONS
80
x
40
60
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SETTING UP PROPORTIONS
80
x
40
60
Match the sides correctly. When not given the name of the triangles, then use either of these proportion.
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SETTING UP PROPORTIONS
80
x
40
60
Match the sides correctly. When not given the name of the triangles, then use either of these proportion.
In this case, what will we use?
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SETTING UP PROPORTIONS
80
x
40
60
Match the sides correctly. When not given the name of the triangles, then use either of these proportion.
In this case, what will we use?
So plug it in,
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SETTING UP PROPORTIONS
80
x
40
60
Match the sides correctly. When not given the name of the triangles, then use either of these proportion.
Put the short sides together and the long sides togetheror =
In this case, what will we use?
So plug it in,
= =
Cross-multiply and solve for x
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SETTING UP PROPORTIONS
80
x
40
60
=
80(x) = 60(40)
80x = 2400
x = 30
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PROVING TRIANGLES ARE SIMILAR
Remember the 3 properties we use for similar triangles.
AA SAS SSS
When solving for questions like this, make sure the ratios equal each other.Don’t guess.
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PROVING TRIANGLES ARE SIMILARWhich similarity theorem or postulate proves the triangles similar?
12
3
9
5
12
9
10
2
4
5
48o
52o
52o
48o
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EXAMPLES
80
x
50
30
Use the information in the figure shown below to find the length of x.
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EXAMPLES
80
x
50
30
Use the information in the figure shown below to find the length of x.
40
Use Pythagoren Theorem to find missing side of smaller triangle
502 – 302 = 402
(Must make sure you keep corresponding parts together!!!!)
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EXAMPLES
80
x
50
30
Use the information in the figure shown below to find the length of x.
Set up proportion:
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EXAMPLES
80
x
50
30
Use the information in the figure shown below to find the length of x.
Set up proportion:
Solve for x:
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EXAMPLES
80
x
50
30
Use the information in the figure shown below to find the length of x.
Set up proportion:
Solve for x: 50(80) = 40x x = 100
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EXAMPLES
180
x
40
60
Use the information in the figure shown below to find the length of x. The two triangles are similar.
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EXAMPLES
180
x
40
60
Use the information in the figure shown below to find the length of x.The two triangles are similar.
Set up proportion:
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EXAMPLES
180
x
40
60
Use the information in the figure shown below to find the length of x.The two triangles are similar.
Set up proportion:
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EXAMPLES
180
x
40
60
Use the information in the figure shown below to find the length of x.The two triangles are similar.
Set up proportion:
Solve for x:
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EXAMPLES
180
x
40
60
Use the information in the figure shown below to find the length of x.The two triangles are similar.
Set up proportion:
Solve for x: 100x = 180(40)
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EXAMPLES
180
x
100
90
Use the information in the figure shown below to find the length of GJ.The two triangles are similar.
S
R
J
G H
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EXAMPLES
180
x
100
90
Use the information in the figure shown below to find the length of GJ.The two triangles are similar.
Set up proportion:
S
R
J
G H
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EXAMPLES
180
x
100
90
Use the information in the figure shown below to find the length of GJ.The two triangles are similar.
Set up proportion:
S
R
J
G H
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EXAMPLES
180
x
100
90
Use the information in the figure shown below to find the length of GJ.The two triangles are similar.
Set up proportion:
Solve for x:
S
R
J
G H
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EXAMPLES
180
x
100
90
Use the information in the figure shown below to find the length of GJ.The two triangles are similar.
Set up proportion:
Solve for x: 90 (x + 100) = 180(x)
S
R
J
G H
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PROVING TRIANGLES ARE SIMILARWhich graph below correctly shows ΔGHJ ~ ΔLMN WITH =
L
HG
M
N
J
10
2
4
5
L
H
G
M
N
J
L
HG
M
N
J
18
12
6
5
20
15
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EXAMPLE
A large ad in the newspaper is 12 cm by 18cm. The next smallest size is reduced by a scale factor of 2/3. What is the size of the reduced ad?
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EXAMPLE
A large ad in the newspaper is 12 cm by 18cm. The next smallest size is reduced by a scale factor of 2/3. What is the size of the reduced ad?
Set up ratio of large ad:
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EXAMPLE
A large ad in the newspaper is 12 cm by 18cm. The next smallest size is reduced by a scale factor of 2/3. What is the size of the reduced ad?
Set up ratio of large ad:
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EXAMPLE
A large ad in the newspaper is 12 cm by 18cm. The next smallest size is reduced by a scale factor of 2/3. What is the size of the reduced ad?
Set up ratio of large ad:
Multiply ratio by the scale factor:
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EXAMPLE
A large ad in the newspaper is 12 cm by 18cm. The next smallest size is reduced by a scale factor of 2/3. What is the size of the reduced ad?
Set up ratio of large ad:
Multiply ratio by the scale factor:
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EXAMPLE
A large ad in the newspaper is 12 cm by 18cm. The next smallest size is reduced by a scale factor of 2/3. What is the size of the reduced ad?
Set up ratio of large ad:
Multiply ratio by the scale factor:
=
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EXAMPLE
A flag is 6 feet by 12 feet, and is made into a bigger flag measured 21 feet by 42 feet. What is the scale factor used to enlarge the flag?
A) 2/1 B) 7/2 C) 2/7 D) 7
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EXAMPLE
A flag is 6 feet by 12 feet, and is made into a bigger flag measured 21 feet by 42 feet. What is the scale factor used to enlarge the flag?
A) 2/1 B) 7/2 C) 2/7 D) 7
Get your original ratio:
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EXAMPLE
A flag is 6 feet by 12 feet, and is made into a bigger flag measured 21 feet by 42 feet. What is the scale factor used to enlarge the flag?
A) 2/1 B) 7/2 C) 2/7 D) 7
Get your original ratio:
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EXAMPLE
A flag is 6 feet by 12 feet, and is made into a bigger flag measured 21 feet by 42 feet. What is the scale factor used to enlarge the flag?
A) 2/1 B) 7/2 C) 2/7 D) 7
Get your original ratio:
Multiply the answer choices to the ratio: (Reminder: Multiply the scale factor to both the numerator and the
denominator)
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EXAMPLE
A flag is 6 feet by 12 feet, and is made into a bigger flag measured 21 feet by 42 feet. What is the scale factor used to enlarge the flag?
A) 2/1 B) 7/2 C) 2/7 D) 7
Get your original ratio:
Multiply the answer choices to the ratio: (Reminder: Multiply the scale factor to both the numerator and the
denominator)
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EXAMPLE
A flag is 6 feet by 12 feet, and is made into a bigger flag measured 21 feet by 42 feet. What is the scale factor used to enlarge the flag?
A) 2/1 B) 7/2 C) 2/7 D) 7
Get your original ratio:
Multiply the answer choices to the ratio: (Reminder: Multiply the scale factor to both the numerator and the
denominator)