Download Practice C

LESSON
8.4
NAME _________________________________________________________ DATE ___________
Challenge: Skills and Applications
For use with pages 480–487
1. Refer to the diagram, where VW YZ.
Y
V
a. Write a similarity statement.
X
b. Write a paragraph proof for your result.
W
Z
2. In the diagram, ABCD is a parallelogram.
E
a. Name three triangles that are similar to BEF.
(For each triangle, give the vertices in the correct,
corresponding order.)
F
B
C
b. Write a paragraph proof for your result.
G
A
D
H
In Exercises 3–8, refer to the diagram. Find the coordinates of the missing
point so that the similarity statement is true. (There may be more than one
correct answer.)
3. Given PQR ~ STU, find the coordinates of U.
4. Given PQR ~ VST, find the coordinates of V.
y
P(1, 4)
5. Given PQR ~ SWT, find the coordinates of W.
2
6. Given PQR ~ TSX, find the coordinates of X.
7. Given PQR ~ YTS, find the coordinates of Y.
R(3, 1)
Q(1, 1)
S(0, 0) 3 T(6, 0) x
8. Given PQR ~ TZS, find the coordinates of Z.
9. Determine if the following conjecture is true or false. If it is true, write a paragraph
proof; if it is false, sketch or describe a counterexample.
If the corresponding angles of quadrilaterals ABCD and EFGH are congruent, then
ABCD ~ EFGH.
10. To estimate the radius of the sun, a student punches a tiny hole in a piece of paper
Lesson 8.4
and allows the sun to shine through the hole, forming an image on a screen 200 cm
away. If the image has a radius of 0.6 cm and the student knows that the sun is
150,000,000 km away, what is the student’s estimate of the radius of the sun?
(Illustration is not to scale.)
r
200 cm
150,000,000 km
0.6 cm
image
62
Geometry
Chapter 8 Resource Book
Copyright © McDougal Littell Inc.
All rights reserved.
Answer Key
Chapter 8
Lesson 8.4
Challenge: Skills and Applications
1. a. VWX ~ ZYX b. Sample answer:
Since VW YZ, the Alternate Interior Angles
Theorem gives V Z and W Y. So, by
the AA Similarity Postulate, VWX ~ ZYX.
2. a. AEH, DGH, CGF b. Sample
answer: Prove BEF ~AEH: Since ABCD is a
parallelogram, BC AD. So, by the
Corresponding Angles Postulate, EBF A.
Also, by the Reflexive Property of Congruence,
E E. So by the AA Similarity Postulate,
BEF ~ AEH. Prove BEF ~ DGH: Since
ABCD is a parallelogram, BC AD and AB DC.
So by the Corresponding Angles Postulate,
E DGH and BFE H. So, by the AA
Similarity Postulate, BEF ~ DGH. Prove
BEF ~ CGF: Since ABCD is a parallelogram,
AB DC. So, by the Alternate Interior Angles
Theorem, E CGF. Also, by the Vertical
Angles Theorem, BFE CFG. So, by the AA
Similarity Postulate, BEF ~ CGF.
3. 6, 4, 6, 4 4. 0, 9, 0, 9
54 36
54
36
5. 13, 13, 13, 13 6. 0, 4, 0, 4
24 36
54
36
7. 6, 9, 6, 9 8. 13, 13, 13, 13
9. false; Sample answer: Let ABCD be a square
and let EFGH be a nonsquare rectangle.
10. 450,000 km
LESSON
NAME _________________________________________________________ DATE ___________
8.4
Practice C
For use with pages 480–487
The triangles shown are similar. List all the pairs of congruent angles
and write the statement of proportionality.
1.
A
2.
B
Q
C
3.
S
R
R
M
T
W
T
V
U
L
O
T
N
Determine whether the triangles can be proved similar. If they are
similar, write a similarity statement. If they are not similar, explain why.
4.
Y
5.
T
H
X
72
L
X
6.
G
A
T
18
Z
M
7.
M
N
K
R
D
J
N
8.
P
B
Q
9. U
E
T
C
V
A
M
N
D
O
S
R
The triangles are similar. Find the value of the variables.
10.
11.
x
y
3.5
x
149
7
y
3
7
2
5
10
12. Given: ABC is a right triangle.
Lesson 8.4
Write a paragraph or a two-column proof.
C
AD is an altitude.
D
Prove: ABC ~ DAC
A
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B
Geometry
Chapter 8 Resource Book
57
Answer Key
Chapter 8
Lesson 8.4
Practice C
1. A Q, B R, C T;
ABC ~QRT 2. S UTV,
W UVT, TUV SUW;
SUW ~ TUV 3. R M, L MON,
MNO RTL, RLT ~MON 4. not
enough information 5. yes; LMN ~ HGD
6. yes; XTR ~ KAJ 7. yes;
QNM ~PNO
8. yes; ABC ~ EDC 9. yes;
RSV ~ RTU 10. x 5, y 12149
10
14
11. x 3 , y 3
12.
Statements
Reasons
1. ABC is a right .
1. Given
2. AD is an altitude.
2. Given
3. AD BC
3. Def. of altitude
4. CDA is a right .
4. lines intersect to
5. CAB CDA
6. C C
7. ABC ~ DAC
form right .
5. All right are .
6. Reflexive Prop. of
Congruence
7. AA ~ Postulate
Answer Key
Chapter 8
Lesson 8.4
Practice C
1. A Q, B R, C T;
ABC ~QRT 2. S UTV,
W UVT, TUV SUW;
SUW ~ TUV 3. R M, L MON,
MNO RTL, RLT ~MON 4. not
enough information 5. yes; LMN ~ HGD
6. yes; XTR ~ KAJ 7. yes;
QNM ~PNO
8. yes; ABC ~ EDC 9. yes;
RSV ~ RTU 10. x 5, y 12149
10
14
11. x 3 , y 3
12.
Statements
Reasons
1. ABC is a right .
1. Given
2. AD is an altitude.
2. Given
3. AD BC
3. Def. of altitude
4. CDA is a right .
4. lines intersect to
5. CAB CDA
6. C C
7. ABC ~ DAC
form right .
5. All right are .
6. Reflexive Prop. of
Congruence
7. AA ~ Postulate
Lesson 8.5
LESSON
NAME _________________________________________________________ DATE ___________
8.5
Practice C
For use with pages 488–496
Are the triangles similar? If so, state the similarity and the postulate or
theorem that justifies your answer.
1. A
B
2. F
3. L
G
I
D
H
C
J
E
D
M
K
P
N
Draw the given triangles roughly to scale. Then, name a postulate or
theorem that can be used to prove that the triangles are similar.
4. In ABC, mA 38 and mB 94. In XYZ, mY 94 and
mZ 48.
5. The ratio of AB to XY is 2:3. In ABC, mB 75, and in XYZ,
mY 75. The ratio of BC to YZ is 2:3.
6. In ABC, mB 50, AB 4, and BC 9. In XYZ, mY 50,
XY 2 and YZ 4.5.
Use the diagram shown to complete the statements.
7. mDGE ?
8. mEDG ?
9. FD ?
10. GD ?
11. EG ?
A 2B C
45 2
50
D
13
12. Name the three pairs of triangles
that are similar in the figure.
E
F
10
G
Write a paragraph or a two-column proof.
13. Given: ABC is equilateral.
DE, DF, EF are midsegments.
Prove: ABC ~ FED
14. Given: ABCD is a trapezoid
with AD and BC as bases.
Prove: EAD ~ EBC
A
C
D
D
E
E
C
72
F
A
B
B
Geometry
Chapter 8 Resource Book
Copyright © McDougal Littell Inc.
All rights reserved.
Answer Key
Chapter 8
Lesson 8.5
Practice C
1. yes; ACB~DCE; AA Similarity Postulate
2. no 3. yes; DMP~LMN; SAS Similarity
Theorem
4.
5.
X
X
A
3
38
94
A
48
Y
75
Z
2
Y
94
B
C
B
AA Similarity Postulate
6.
X
2
A
50
4.5
Y
Z
75
2
3
Z
C
SAS Similarity Theorem
7. 45 8. 85
9. 10 10. 102
11. 10 69
4
50
B
9
C
SAS Similarity Theorem
12. ABD~GFD, CBD~EFD,
ACD~GED
13.
Statements
Reasons
1. ABC is equilateral.
1. Given
2. AB BC AC
2. Def. of
3. DE, DF, and EF
are midsegments.
1
1
4. DE 2BC, EF 2AC,
1
DF 2AB
5. ABC~FED
equilateral 3. Given
4. Midsegment
Thm.
5. SSS Similarity
Thm.
14.
Statements
Reasons
1. ABCD is a trapezoid.
1. Given
2. AD and BC are bases.
2. Given
3. AD
3. Def. of base of
BC
4. EDA ECB
5. EAD EBC
6. EAD EBC
trapezoid
4. Corresponding Postulate
5. Corresponding Postulate
6. AA Similarity
Postulate
LESSON
NAME _________________________________________________________ DATE ___________
8.7
Practice C
For use with pages 506–513
Identify the dilation, and find its scale factor. Then, find the values of
the variables.
1.
2. P
P
9
x
P
12.5
5
x
8
P
C
y
4
3
6
4
y
C
3.
7
C
9
4. P
x P
5 P
y
13.5
18.4
7.56
P
C
5
z
12.6
x
5. k 2
3
6. k Lesson 8.7
Use the origin as the center of the dilation and the given scale factor
to find the coordinates of the vertices of the image of the polygon.
5
2
y
y
H
I
N
M
G
1
L
1
x
1
J
1
x
7. You are making hand shadows on a wall using a flashlight. You hold your
hand 1 foot from the flashlight and 5 feet from the wall. Your hand is parallel
to the wall. If the measure from your thumb to ring finger is 6 inches, what
will be the distance between them in the shadow?
Copyright © McDougal Littell Inc.
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Geometry
Chapter 8 Resource Book
103
Answer Key
Chapter 8
Lesson 8.7
Practice C
5
1. The dilation has center C and scale factor 2;
x 20, y 10. 2. The dilation has center C
9
27
27
and scale factor 4; x 4 , y 2 .
2
3. The dilation has center C and scale factor 3;
15
21
15
x 2 , y 2 , z 2 . 4. The dilation has center
C and scale factor 35; x 11.04.
2 4
4 8
5. M 3, 3 , N3, 3 , L4, 0
6. G5, 5, H0, 15, I20, 12.5, J15, 2.5
7. 36 in.
LESSON
NAME _________________________________________________________ DATE ___________
11.3
Practice C
For use with pages 677–682
The polygons shown are similar. Find the ratio (shaded to
unshaded) of their perimeters and of their areas.
1.
2.
22
12
28
5
3.
4.
6
10
5
12
15
Solve.
5. The perimeter of an equilateral triangle is 48 centimeters. A smaller equi-
lateral triangle has a side length of 6 centimeters. What is the ratio of the
areas of the larger triangle to the smaller triangle?
6. The ratio of the areas of two similar triangles is 84:40. What is the ratio of
the lengths of corresponding sides?
7. A pentagon has an area of 128 square centimeters. A similar pentagon has
an area of 180 square centimeters. What is the ratio of the perimeters of
the smaller pentagon to the larger pentagon?
8. The dimensions of a rectangle are 8 centimeters by 12 centimeters. What
are the dimensions of a similar rectangle with exactly double the area?
Lesson 11.3
9. Find the ratio of the areas of the triangles.
10. Find the ratio of area I to area II.
60
24
12
II
I
10
11. Floor plan
The floor plan has a scale of
1 inch to 18 feet.
3
4
a. What is the scale area of the kitchen?
What is the actual area?
b. What is the scale area of the bedroom?
What is the actual area?
1
in.
living
room
1 4 in.
14
1
1 4 in.
dining room
kitchen
bath
3
8
Copyright © McDougal Littell Inc.
All rights reserved.
18
3
8
in.
bedroom
8
30
in.
Geometry
Chapter 11 Resource Book
45
Answer Key
Chapter 11
Lesson 11.3
Practice C
1. 12 :5; 12:25 2. 14:11; 196:121 3. 3:5;
9:25 4. 5:4; 25:16 5. 64:9 6. 21:10
7. 42:35 8. 82 cm by 122 cm
49
1
9. 9:4 10. 4:9 11. a. 64 in.2; 24816 ft2
21
5
b. 64 in.2; 10616 ft2