Embed Size (px)
Citation preview
Chapter 9 Skills Practice • 681
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.1 Skills Practice
!"#$ ________________________________________________________ %"&$ _________________________
Expanding Your MindDilations of Triangles
VocabularyChoose the term or terms from the box to best complete each sentence.
dilation center of dilation scale factor
enlargement reduction dilation factor
1. The , or , is the ratio formed when comparing the distance of the
image from the center of dilation to the distance of the original !gure from the center of dilation.
2. In mathematics, are transformations that produce images that are the same shape as
the original image, but not the same size.
3. When the scale factor is less than one, the image is called a(n) .
4. When the scale factor of a dilation is greater than one, the image is called a(n) .
5. In a dilation, each point on the original !gure is moved along a straight line and the straight line is
drawn from a !xed point known as the .
Problem SetDilate each triangle with P as the center of dilation and the given scale factor.
1. Dilate triangle ABC with P as the center of dilation and a scale factor of 2.
P
A
B
C
A’
B’
C’
682 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.1 Skills Practice page 2
2. Dilate triangle ABC with P as the center of dilation and a scale factor of 3.
P
A
B
C
3. Dilate triangle ABC with P as the center of dilation and a scale factor of 1 __ 2
.
P
A
B
C
4. Dilate triangle ABC with P as the center of dilation and a scale factor of 1 __ 3
.
P
A
B
C
Chapter 9 Skills Practice • 683
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.1 Skills Practice page 3
!"#$ ________________________________________________________ %"&$ _________________________
5. Dilate triangle ABC with P as the center of dilation and a scale factor of 4.
P
A
B
C
6. Dilate triangle ABC with P as the center of dilation and a scale factor of 1 __ 4
.
P
A
B
C
684 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.1 Skills Practice page 4
Dilate each triangle with P as the center of dilation and the given scale factor.
7. Dilate triangle ABC on the coordinate plane using the origin (0, 0) as the center of dilation and a
scale factor of 2.
4
2
420 6 80
10 12 14 16 18 20
6
8
10B’(6,10)
C’(10,4)A’(4,4)
12
14
16
18
20
B(3,5)
A(2,2) C(5,2)
y
x
8. Dilate triangle ABC on the coordinate plane using point A (3, 3) as the center of dilation and a
scale factor of 2.
4
2
420 6 80
10 12 14 16 18 20
6
8
10
12
14
16
18
20
C(3,7)
A(3,3) B(9,3)
y
x
Chapter 9 Skills Practice • 685
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.1 Skills Practice page 5
!"#$ ________________________________________________________ %"&$ _________________________
9. Dilate triangle ABC on the coordinate plane using the origin (0, 0) as the center of dilation and a
scale factor of 1 __ 2
.
4
2
420 6 80
10 12 14 16 18 20
6
8
10
12
14
16
18
20y
x
B(8,12)
A(4,4)C(12,4)
10. Dilate triangle ABC on the coordinate plane using the origin (0, 0) as the center of dilation and a
scale factor of 1 __ 2
.
4
2
420 6 80
10 12 14 16 18 20
6
8
10
12
14
16
18
20y
x
B(10,18)
A(8,10) C(16,10)
686 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.1 Skills Practice page 6
11. Dilate triangle ABC on the coordinate plane using point A (2, 1) as the center of dilation and a scale
factor of 3.
4
2
420 6 80
10 12 14 16 18 20
6
8
10
12
14
16
18
20
C(4,1)A(2,1)
B(2,6)
y
x
12. Dilate triangle ABC on the coordinate plane using point A (3, 3) as the center of dilation and a scale
factor of 1 __ 3 .
4
2
420 6 80
10 12 14 16 18 20
6
8
10
12
14
16
18
20
C(15,3)A(3,3)
B(3,18)
y
x
Chapter 9 Skills Practice • 687
© 2
011
Car
negi
e Le
arni
ng
Look-AlikesSimilar Triangles
VocabularyDe!ne the term in your own words.
1. similar triangles
Problem SetIdentify the congruent corresponding angles and write ratios to identify the proportional sides of the
similar triangles in each problem.
1. nABC , nA9B9C9
P
A
B
C
A’
B’
C’
Congruent corresponding angles:
/A > /A9
/B > /B9
/C > /C9
Proportional Sides:
AB ____ A9B9 5 BC ____ B9C9
5 CA ____ C9A9
Lesson 9.2 Skills Practice
!"#$ ________________________________________________________ %"&$ _________________________
688 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.2 Skills Practice page 2
2. nDEF , nD9E9F9
P
D
E
F
D’
E’
F’
3. nABC , nDEF
P
A
B
C
D
E
F
Chapter 9 Skills Practice • 689
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.2 Skills Practice page 3
!"#$ ________________________________________________________ %"&$ _________________________
4. nFGH , nXYZ
P
X
Y
Z
F
G
H
5. nABC , nMNP
690 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.2 Skills Practice page 4
6. nRST , nXYZ
7. nXYZ , nGHJ
8. nKLM , nRST
Chapter 9 Skills Practice • 691
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.2 Skills Practice page 5
!"#$ ________________________________________________________ %"&$ _________________________
Determine each missing measure.
9. Given: nACE , nBCD
E
C
D
10 cmA
B5 cm
?
4 cm
BD ___ AE
5 CD ____ CE
5 cm ______ 10 cm
5 4 cm _____ x
5x 5 10(4)
5x 5 40
x 5 8
CE 5 8 cm
CD 1 DE 5 CE
4 cm 1 DE 5 8 cm
DE 5 4 cm
692 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.2 Skills Practice page 6
10. Given: nNMR , nNPQ
103°
QR
M
N
P?
11. Given: nRTU , nRSV
VU
S
R
T?
42°
Chapter 9 Skills Practice • 693
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.2 Skills Practice page 7
!"#$ ________________________________________________________ %"&$ _________________________
12. Given: nNYZ , nMYX
X
Y
Z
M
N
3 cm
?
6 cm
6 cm
694 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.2 Skills Practice page 8
13. Given: nABC , nXYZ
Y
XZ
B
A C
24 cm
?
36 cm
8 cm
14. Given: nNMP , nXYZ
X
Y
Z
N P
2 cm
4 cm
12 cm
?
M
Chapter 9 Skills Practice • 695
© 2
011
Car
negi
e Le
arni
ng
Prove It!AA, SAS, and SSS Similarity Theorems
VocabularyDe!ne each theorem in your own words.
1. SAS Similarity Theorem
2. AA Similarity Theorem
3. SSS Similarity Theorem
Lesson 9.3 Skills Practice
!"#$ ________________________________________________________ %"&$ _________________________
696 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.3 Skills Practice page 2
Problem SetDetermine if the triangles in each problem are similar.
1. Use the AA Similarity Theorem and a protractor to determine if nABC and nA9B9C9 are
similar triangles.
4
2
420 6 80
10 12 14 16 18 20
6
8
10
12
14
16
18
20
C
A
A’
B’ C’
B
y
x
The measures of /A and /A9 are equal.
Angle B and /B9 are both right angles.
The measures of /B and /B9 are equal.
The two triangles are similar by the AA Similarity Theorem.
2. Use the AA Similarity Theorem and a protractor to determine if nABC and nA9B9C9 are
similar triangles.
4
2
420 6 80
10 12 14 16 18 20
6
8
10
12
14
16
18
20
CA
A’
B’
C’B
y
x
Chapter 9 Skills Practice • 697
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.3 Skills Practice page 3
!"#$ ________________________________________________________ %"&$ _________________________
3. Use the SAS Similarity Theorem and a protractor to determine if nABC and nA9B9C9 are
similar triangles.
4
2
420 6 80
10 12 14 16 18 20
6
8
10
12
14
16
18
20
A (2,7)
A’ (13,13) C’ (17,13)
B’ (13,15)
C (10,7)
B (2,11)
y
x
698 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.3 Skills Practice page 4
4. Use the SAS Similarity Theorem and a protractor to determine if nABC and nA9B9C9
are similar triangles.
4
2
420 6 80
10 12 14 16 18 20
6
8
10
12
14
16
18
20
A (2,8)
A’ (11.5,2)
C (8,8)
C’ (14.5,2)
B (5,18)
B’ (13,7)
y
x
Chapter 9 Skills Practice • 699
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.3 Skills Practice page 5
!"#$ ________________________________________________________ %"&$ _________________________
5. Use the SSS Similarity Theorem to determine if nABC and nA9B9C9 are similar triangles.
4
2
420 6 80
10 12 14 16 18 20
6
8
10
12
14
16
18
20
A (3,3)
A’ (14,7)
C (7,11)
C’ (15,9)
B (11,3)
B’ (16,7)
y
x
700 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.3 Skills Practice page 6
6. Use the SSS Similarity Theorem to determine if nABC and nA9B9C9 are similar triangles.
4
2
420 6 80
10 12 14 16 18 20
6
8
10
12
14
16
18
20
A (2,2)
A’ (11,13)
B (2,11)
C’ (15,13)
C (14,2)
B’ (11,10)
y
x
Chapter 9 Skills Practice • 701
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.3 Skills Practice page 7
!"#$ ________________________________________________________ %"&$ _________________________
Determine if the triangles in each are similar by AA, SAS, or SSS.
7.
95° 95°
The triangles are similar by AA.
8.
14 cm
23°
14 cm
7 cm 7 cm23°
9.
6 cm
7 cm3 cm
3.5 cm
702 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.3 Skills Practice page 8
10.
5 cm
10 cm
6 cm
6 cm
6 cm
6 cm
11.
5.5 cm
2 cm
1 cm
11 cm
4 cm
2 cm
12.
42°42°
Chapter 9 Skills Practice • 703
© 2
011
Car
negi
e Le
arni
ng
Back on the GridSimilar Triangles on the Coordinate Plane
Problem SetVerify that the triangles in each are similar.
1. Triangle DEF is the image that resulted from a dilation of nABC. Use the SAS Similarity Theorem to
determine whether nABC is similar to nDEF.
Lesson 9.4 Skills Practice
!"#$ ________________________________________________________ %"&$ _________________________
4
2
420 6 80
10 12 14 16 18 20
6
8
10
12
14
16
18
20y
x
A (2,3)C (6,3)
B (2,5)
E (4,10)
D (4,6)F (12,6)
Corresponding Sides ___
AB and ___
DE :
AB 5 2
DE 5 4
DE ___ AB
5 4 __ 2
5 2
Corresponding Sides ___
AC and ___
DF :
AC 5 4
DF 5 8
DF ___ AC
5 8 __ 4
5 2
DE ___ AB
5 DF ___ AC
5 2
Corresponding Angles /A and /D:Angle A and /D are both right angles.The measures of /A and /D are equal.
The two triangles are similar by the SAS Similarity Theorem.
704 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.4 Skills Practice page 2
2. Triangle DEF is the image that resulted from a dilation of nABC. Use the SAS Similarity Theorem
and a protractor to determine whether nABC is similar to nDEF.
4
2
420 6 80
10 12 14 16 18 20
6
8
10
12
14
16
18
20y
x
A (8,10)
B (12,18)
D (4,5)
E (6,9)
F (8,5)
C (16,10)
Chapter 9 Skills Practice • 705
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.4 Skills Practice page 3
!"#$ ________________________________________________________ %"&$ _________________________
3. Triangle DEF is the image that resulted from a dilation of nABC. Use the SSS Similarity Theorem to
determine whether nABC is similar to nDEF.
4
2
420 6 80
10 12 14 16 18 20
6
8
10
12
14
16
18
20
A (2,10) C (8,10)
B (8,18)
D (5,2)
E (17,18)
F (17,2)
y
x
706 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.4 Skills Practice page 4
4. Triangle DEF is the image that resulted from a dilation of nABC. Use the SSS Similarity Theorem to
determine whether nABC is similar to nDEF.
4
2
420 6 80
10 12 14 16 18 20
6
8
10
12
14
16
18
20
A (1,11)
C (6,1)
B (11,11) D (13,11)
F (15.5,6)
E (18,11)
y
x
Chapter 9 Skills Practice • 707
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.4 Skills Practice page 5
!"#$ ________________________________________________________ %"&$ _________________________
5. Dilate nABC to form nDEF using point P (0, 0) as the center of dilation and a scale factor of 2.
Use the AA Similarity Theorem and a protractor to determine whether nABC is similar to nDEF.
4
2
420 6 80
10 12 14 16 18 20
6
8
10
12
14
16
18
20y
xA (2,1)
P (0,0)
B (2,10)
C (6,1)
708 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.4 Skills Practice page 6
6. Dilate nABC to form nDEF using point P (0, 0) as the center of dilation and a scale factor of 1 __ 2
.
Use the AA Similarity Theorem and a protractor to determine whether nABC is similar to nDEF.
4
2
420 6 80
10 12 14 16 18 20
6
8
10
12
14
16
18
20y
x
A (9,8)
B (12,18)
C (18,12)
P (0,0)
Chapter 9 Skills Practice • 709
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.4 Skills Practice page 7
!"#$ ________________________________________________________ %"&$ _________________________
7. Dilate DABC to form nDEF using point A (2, 3) as the center of dilation and a scale factor of 3.
Use the SAS Similarity Theorem to determine whether nABC is similar to nDEF.
4
2
420 6 80
10 12 14 16 18 20
6
8
10
12
14
16
18
20
A (2,3)C (7,3)
B (2,8)
y
x
710 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.4 Skills Practice page 8
8. Dilate nABC to form nDEF using point A (0, 2) as the center of dilation and a scale factor of 1 __ 3
.
Use the SAS Similarity Theorem to determine whether nABC is similar to nDEF.
4
2
420 6 80
10 12 14 16 18 20
6
8
10
12
14
16
18
20
A (0,2)
C (18,2)
B (9,14)
y
x
