Name ———————————————————————
Date ————————————
Practice C
LESSON
6.3
For use with pages 387–395
List all pairs of congruent angles for the polygons. Then write the ratios of
the corresponding sides in a statement of proportionality.
1. n STU , n CDE
2. n LMN , n GHI
3. quadrilateral CDEF , quadrilateral MNKL
Determine whether the polygons are similar. If they are, write a similarity
statement and find the scale factor of Figure A to Figure B.
4. L
O
4.5
B
12
8
5.
P
9
B
C
A
6
A
12.8
F
G
8
B
E
D
5
H
A
M
8
T
6
N
In the diagram at the right, quadrilateral BCDE , quadrilateral WXYZ.
6. Find the scale factor of quadrilateral BCDE to
B
quadrilateral WXYZ.
C
3
E
quadrilateral BCDE.
6
D
Y
Z
9. Find m∠ C.
10. Find the perimeter of quadrilateral WXYZ.
117�
X
6
W
Use the given information to find the indicated value.
11. GIVEN: n CDX , n GNZ, the perimeter of n CDX is 48 feet, CX 5 14 feet, and
GZ 5 58.8 feet.
LESSON 6.3
Find the perimeter of n GNZ.
392
12. GIVEN: n ABC , n DEF, n ABC is isosceles, n ABC has a perimeter of 18 inches
and a leg of length 5 inches, and the base of n DEF is 34.4 inches long.
Find the perimeter of n DEF.
Geometry
Chapter 6 Resource Book
Copyright © Holt McDougal. All rights reserved.
7. Find the scale factor of quadrilateral WXYZ to
8. Find XY.
4
Name ———————————————————————
Practice C
LESSON
6.3
For use with pages 387–395
Date ————————————
continued
Quadrilateral KLMN , quadrilateral WXYZ.
Find the indicated length in terms of
r, s, t, u, and v.
r
13. WX
K u
L
s
M
X
t
Y
N
14. XY
v
W
15. YZ
Z
Find all possible values of x in the similar triangles.
16. n FGH , n JKL
G
17. n PQR , n STU
5x
3x � 2
P
H
13 � x
F
K
S
7�x
T
Q
7x
x2
L
5x � 2
� 20
x2
�5
J
U
R
18. n CDE , n FGH
19. n LMK , n KMN
N
G
D
7x
C
8x 2 1
9x
14x 1 6
10x 1 1
L
E
F
H
9x
17x 1 5
K
27x 1 11
20. Shuffleboard The game of outdoor shuffleboard
is played on a hard, smooth surface such as concrete.
From a distance, players slide large, 6-inch pucks
toward a triangular scoring region, as shown in the
figure at the right. At the end of each round, any puck
lying entirely within the lines of a scoring region scores
the number of points indicated (7, 8, or 10).
The scoring region contains two similar triangles.
The scale factor of the large triangle (containing all
five regions) to the small triangle (the 10-point region)
is 3 : 1. How many times greater is the total area of the
7- and 8-point regions than the area of the 10-point region?
10
8
7
8
LESSON 6.3
Copyright © Holt McDougal. All rights reserved.
M
7
Geometry
Chapter 6 Resource Book
393
3
1
5. n ABC , n FDE; } 6. GHIJ , KLMN; }
2
2
1
7. not similar 8. n ABC , n FDE; } 9. 8
1
3
10. 18 11. }; P(n LMN) 5 45, P(n PQR) 5 60
4
3
12. }; P(XYZW) 5 100, P(STUV) 5 60
5
13. altitudes; x 5 24 14. medians; y 5 12
15. The shadow is not similar to the kite because
the corresponding side ratios are not all the same:
95
78
142
132
} < 1.22 Þ 1.08 ø }
Practice Level B
1. ∠ A > ∠ D, ∠ B > ∠ F, ∠ C > ∠ E,
BC
FE
AB
DF
AC
DE
} 5 } 5 } 2. ∠ W > ∠ M, ∠ X > ∠ N,
WX
XY
YZ
WZ
5}
5}
5}
∠ Y > ∠ O, ∠ Z > ∠ P, }
MP
NO
OP
MN
1
3. C 4. no 5. yes; BCDA , WXYZ; } or
4
WXYZ , BCDA; 4
5
4
6. } 7. 15, 8, 135 8. 40 9. 50 10. }
5
4
11. m 5 11, n 5 4 12. m 5 8 13. XY 5 30 in.,
2
21 in. 14. 9.75 in. 15. C 16. }5
17. XY 5 3.6, PN 5 15 18. 2.32
19. Area of n XYZ 5 6.96; Area of
nMNP 5 43.5; The area of similar triangles differ
by the scale factor squared.
3
5
20. } 21. 60 ft 22. 3200 ft2
Practice Level C
1. ∠ S > ∠ C, ∠ T > ∠ D, ∠ U > ∠ E;
ST
TU
SU
}5}5}
DE
CD
CE
2. ∠ L > ∠ G, ∠ M > ∠ H, ∠ N > ∠ I;
MN
LN
LM
}5}5}
HI
GH
GI
3. ∠ C > ∠ M, ∠ D > ∠ N, ∠ E > ∠ K,
CD
CF
DE
EF
∠ F > ∠ L; }
5}
5}
5}
MN
NK
KL
ML
4
4. n LNM , n TPO; }
3
5
5. quadrilateral ABCD , quadrilateral HEFG; }
8
3
2
6. } 7. } 8. 4.5 9. 1178 10. 24 11. 201.6 ft
3
2
rv
sv
tv
12. 77.4 in. 13. } 14. } 15. } 16. 6
u
u
u
A70
Geometry
Chapter 6 Resource Book
17. 25, 2.5 18. 8 19. 20.4, 15
20. 8 times greater
Review for Mastery
9
5
1. } 2. 36 3. } 4. 77.5 5. 20
10
4
Problem Solving Workshop:
Mixed Problem Solving
1. a. 58,800 yen b. about 580.56 Canadian
2
dollars 2. a. }7, x 5 45.5, y 5 17.5 b. 50, 175
c. 60, 735 d. The ratio of the perimeters is equal
to the scale factor. The ratio of the areas is equal
to the square of the scale factor. 3. 517
4. a. 3.12 in. b. 15 5. 3.2 6. Answers will
vary. 7. a. 10.6 lb per person b. 42.4 lb; about
3.53 lb c. about 11 oranges d. Sample answer:
No; Some families eat more fruits than others.
The oranges could have been used in recipes.
Challenge Practice
7
1. } 2. 21 cm 3. JK 5 35 cm, JL 5 36.75 cm,
4
RS 5 20 cm, ST 5 13 cm, RT 5 21 cm
4. Area of n JKL 5 385.875 cm2;
Area of n RST 5 126 cm2; 3.06251;
The scale factor of the areas is the square of the
scale factor of the perimeters.
5. Sample answer: A
40
B
1
C
E
G
ABDC > CDFE > EFHG
40
6. Sample answer: A
C
13 3
D
1
13 3
F
1
13 3
H
B
10
D
20
E
G
F
10
H
ABDC , CDFE; CDFE , EFHG, (ABDC >
EFHG)
Copyright © Holt McDougal. All rights reserved.
ANSWERS
Lesson 6.3, continued