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)