48
SIMILAR TEST REVIEW STUDY, STUDY, STUDY!!!
SIMILAR TEST REVIEW
STUDY, STUDY, STUDY!!!
HOW CAN A RATIO BE WRITTEN?
HOW CAN A RATIO BE WRITTEN?
a : b
and
a/b
HOW CAN A RATIO BE WRITTEN?
a : b
and
a/b
READS: A TO B
What is the definition of aPROPORTION?
What is the definition of aPROPORTION?
is an equation showing that two ratios are
EQUALto each other.
WHAT PROPERTIES AND THEOREMS ARE USED FOR PROVING SIMILAR TRIANGLES?
WHAT PROPERTIES AND THEOREMS ARE USED FOR PROVING SIMILAR TRIANGLES?
AASSSSAS
SOLVING PROPORTIONS
1. 2.
SOLVING PROPORTIONS
1. 2.
10(4) = 8(k) CROSS-MULTIPLY 1(99) = 9(X – 9)
SOLVING PROPORTIONS
1. 2.
10(4) = 8(k) CROSS-MULTIPLY 1(99) = 9(X – 9)
40 = 8K MULTIPLY TERMS 99 = 9X - 81
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
SETTING UP PROPORTIONS
80
x
40
60
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.
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?
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,
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
SETTING UP PROPORTIONS
80
x
40
60
=
80(x) = 60(40)
80x = 2400
x = 30
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.
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
EXAMPLES
80
x
50
30
Use the information in the figure shown below to find the length of x.
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!!!!)
EXAMPLES
80
x
50
30
Use the information in the figure shown below to find the length of x.
Set up proportion:
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:
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
EXAMPLES
180
x
40
60
Use the information in the figure shown below to find the length of x. The two triangles are similar.
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:
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:
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:
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)
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
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
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
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
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
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
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?
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:
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:
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:
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:
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:
=
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
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:
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:
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)
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)
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)
