Name ———————————————————————
Date ————————————
Chapter Test A
CHAPTER
5
For use after Chapter 5
}
WY is the midsegment of nQRS. Find the value of x. 1.
2.
R W
1.
R
x
34 Q
Y
3.
S
S
3. Q
Y
4.
R
15
x W
2.
W
22
x
Answers
R
5.
8 Y
6.
x
W
Y
7.
12 Q
S
8.
S
9.
Find the coordinates of point M in the figure. 5.
6.
y
4.
10.
y
(h, 2k)
M
(0, 0)
x
M (0, 0)
x
Find the value of x. 7.
X
Z
8. A
B
Y 2x
16
E
6x 2 8
x12
D
W C
Use the information in the diagram to find x. 9.
10. m∠ ABC 5 908.
M 258
N
L Q (x 1 10)8
A 12 B
458 C
90
Geometry Chapter 5 Assessment Book
D
x28
Copyright © Holt McDougal. All rights reserved.
(2h, k)
Name ———————————————————————
Chapter Test A
CHAPTER
5
Date ————————————
continued
For use after Chapter 5
In n ABC, Q is the centroid. 11. QC 5 12. Find CM. L
C
12. QC 5 6. Find CL.
11.
B
A
Q
N
Answers
12. 13.
M
L
M
14.
Q C
N
A
B
15.
List the unknown sides or angles in order from smallest to largest.
16.
13.
17.
14.
R
B
858 24 408
Q
558
18.
30
19.
S 18
C
20.
A
Is it possible to construct a triangle with the given side lengths? 15. 3, 7, 9
16. 4, 6, 10
17. 2, 7, 10
Complete with <, >, or 5.
?
Copyright © Holt McDougal. All rights reserved.
18. AB
BC
A
19. RS
? VW V
C
B
R 458 208
D
T
308 Q
508
W
S
20. Arrange statements A–D in order to write an indirect proof of the
statement: If x 1 y Þ 10 and x 5 9, then y Þ 1. A. But this contradicts the given statement that x 1 y Þ 10. B. x 1 y 5 9 1 1 5 10 C. Temporarily assume that y 5 1. D. The contradiction shows that the temporary assumption that
y 5 1 is false. This proves that y Þ 1.
Geometry Chapter 5 Assessment Book
91
Name ———————————————————————
Date ————————————
Chapter Test B
CHAPTER
5
For use after Chapter 5
}
WY is the midsegment of nQRS. Find the value of x. 1.
2.
R
W
3.
x 2 16 S
Y
S
Y
4.
R 2x W
2.
W
30
19
4.
See left.
6.
See left.
R
3
Y
W
2x 1 8
Y
14 S
S
Place the figure in a coordinate plane in a convenient way. Give the coordinates of each vertex. 5. Isosceles right triangle:
7.
6. Rectangle: Length is 3 and
Leg length is 3.
8.
width is 2.
y
y
1
1 x
1
x
1
In the diagram, the perpendicular bisectors of nWXY meet at point Z. Find the indicated measure. 7. WZ
8. ZY
X
5
Z
W
8
X
9 Z 7
3 W
92
5.
Geometry Chapter 5 Assessment Book
4
Y
Y
Copyright © Holt McDougal. All rights reserved.
3.
1.
R
28
x 1 10
Answers
Name ———————————————————————
Chapter Test B
CHAPTER
5
For use after Chapter 5
Date ————————————
continued
Use the information in the diagram to find x. 9.
Answers
10.
9.
x 1 12
3x 2 5
10.
458 458
2x 1 2
11. 2(x 1 10)
12. 13.
In n ABC, Q is the centroid. Find the indicated length. 11. QC 5 12. Find QM. L
C
15.
B
A
N
14.
12. QC 5 6. Find QL.
M
16.
M
L
17. A
B
C
N
18.
List the unknown sides in order from smallest to largest. 13.
14.
B
R 298
858
Copyright © Holt McDougal. All rights reserved.
508 A
C S
15. A triangle has one side of length 10 and another of length 6.
Describe the possible lengths of the third side. Complete with <, >, or 5. 16. AB
?
BC
17. RS
?
VU V
C A 458
B 1108
648
R
308 D
T 508
708
U
S
18. Suppose you wanted to prove the statement “If x 1 y . 20 and
y 5 5, then x . 15.” What temporary assumption could you make to prove the conclusion indirectly? Geometry Chapter 5 Assessment Book
93
Name ——————————————————————— CHAPTER
5
Date ————————————
Chapter Test C For use after Chapter 5
Answers
E
Use nDEF, where J, K, and L are midpoints of the sides.
1.
1. If DE 5 8x 1 12 and KL 5 10x 2 9,
J
what is DE?
2.
K
2. If JL 5 7x 2 6 and EF 5 9x 1 8,
3.
what is EK? D
3. If DF 5 18x 2 6 and JK 5 3x 1 11,
L
F
4.
what is JK?
5.
Find the value of x.
6.
4.
5.
G
(
5 x 8
(x 2 11)8
)
7.
178
8. 9. F J 3x 1 10
7 x 2
H 15
10.
Find the value of x that makes P the incenter of the triangle. 6.
7.
B
11. 12.
Z
3x 1 1 7x 2 4 W
P A
34 H 30
X P 117
C
R
108
Y
Q
Find the coordinates of the centroid P of nSTU. 8. S(2, 5), T(5, 22), U(21, 26) 9. S(21, 7), T(5, 26), U(27, 24)
Point S is the centroid nPQR. Use the given information to find the value of x. 10. QS 5 3x 1 5 and QT 5 4x 1 11
U
P
S
11. VS 5 3x 2 2 and VP 5 7x 1 4 12. RS 5 4x 1 1 and SU 5 3x 2 4
T
V R
94
Geometry Chapter 5 Assessment Book
Q
Copyright © Holt McDougal. All rights reserved.
G
F
Name ———————————————————————
Chapter Test C
CHAPTER
5
Date ————————————
continued
For use after Chapter 5
Answers
13. In the space below, construct a circle through three
noncollinear points.
13.
See left.
14.
15.
List the sides and the angles in order from smallest to largest. 14. A
C
418
15.
16.
F 56
30
17. G
48
H B
18.
Is it possible to build a triangle using the given side lengths? If so, order the angle measures of the triangle from least to greatest. }
}
}
}
}
16. AB 5 Ï 73 , BC 53Ï 10 , AC 5 5Ï 7
20. 21.
}
17. JK 5 Ï 33 , KL 5 4Ï 5 , JL 5 9Ï 3 Copyright © Holt McDougal. All rights reserved.
19.
Complete the statement with <, >, or 5. 18. m ∠1
?
m∠2
19. PQ
?
SR Q
10 5
2
1
R
6 17 P S
Use the Hinge Theorem or its converse and properties of triangles to write and solve an inequality to describe a restriction on the value of x. 20.
21.
12
7
10 (3x 1 8)8
x 1 11
16 718
1058 348 5x 2 7
948
7
10
Geometry Chapter 5 Assessment Book
95
Chapter 4, continued
e.
y
B(0, 4) E(0, 4)
C(21, 1) A(23, 0)
1 D(3, 0)
6.
y
y
1
1 1
x
1
x
(0, 0), (0, 3), (3, 0)
(0, 0), (0, 2), (3, 2), (3, 0) 7. 5 8. 9 9. 10 10. 25 11. 6 12. 3 } } } } } } 13. BC, AB, AC 14. QS, QR, RS 15. 4 < x < 16 16. < 17. > 18. x ≤ 15 Chapter Test C 1. 32 2. 22 3. 18 4. x 5 10 5. x 5 48
F(1, 1)
1
5.
ANSWERS
illustrates the student’s explanation of when to use the method. 2. a. n ABD and nCBD are scalene right triangles; n ABC is an acute isosceles triangle; nEFG is an obtuse scalene triangle b. It is given that n ABD and nCBD are right triangles and } } } } AB > CB. By the Reflexive Property, BD > BD. So, by the HL Congruence Theorem, n ABD > nCBD. c. ∠ BAD > ∠ BCD; } } ∠ ABD > ∠ CBD; ∠ ADB > ∠ CDB; AB > CB; } } } } BD > BD; AD > CD d. 1148
x
6. x 5 5 7. x 5 7 8. (2, 21) 9. (21, 21)
9 10. x 5 7 11. x 5 5 12. x 5 } 2
} } }
13. Check students’ drawings 14. BC, AC, AB 15. ∠ G, ∠ F, ∠ H f. reflection in y-axis g. Sample answer: Use the
Distance Formula to find the side lengths of all three triangles. Then use the SSS Congruence Postulate.
16. yes; ∠ C, ∠ A, ∠ B 17. no 18. <
9 19. 5 20. x < 21 21. x < } 2
Copyright © Holt McDougal. All rights reserved.
Standardized Test A
Chapter 5
1. D 2. B 3. D 4. C 5. A 6. B 7. A 8. C
Quiz 1
9. A 10. A 11. D 12. B 13. 6
1. 19 2. 12 3. 8 4. 10; Perpendicular Bisector Theorem 5. 14; Concurrency of
14. CM . 5 and CM , 17
Perpendicular Bisectors Theorem
is Ï 92 1 122 5 15 miles. b. The tower and the fires form a triangle and the shortest distance between the campgrounds is a midsegment of the triangle. It is parallel to the side measuring 15 miles, so its distance is 7.5 miles. c. 4.5 miles; The path is the midsegment that is parallel to the side between the tower and Fire 1, which measures 9 miles.
Quiz 2 1. 7 2. 7 3. 6 4. 12 5. 4
Quiz 3 1. yes 2. No, 4 1 7 < 13. 3. 1 < x < 11
} } }
4. 7 < x < 35 5. BC, AC, AB 6. ∠ D, ∠ E, ∠ F 7. < 8. 5
Chapter Test A 1. 68 2. 11 3. 12 4. 7.5 5. (2h, 0)
h 6. }, k 7. 8 8. 2 9. 15 10. 20 11. 18 2 } } } 12. 9 13. RS, RQ, QS 14. ∠ B, ∠ A, ∠ C
1
2
15. yes 16. no 17. no 18. < 19. > 20. C, B, A, D
Chapter Test B 3 1. 50 2. 30 3. 7 4. } 4
15. a. By the Pythagorean Theorem, the distance }
Standardized Test B 1. B 2. D 3. B 4. C 5. A 6. A 7. D 8. B 9. A 10. B 11. C 12. A 13. 43 14. 11 < QR < 29 15. a. 141.4 yd b. By the Pythagorean Theorem, a2 1 b2 5 c2, so
502 1 502 5 c2 and c < 70.7. By the Midsegment Theorem, because the pool and laundry room are midpoints, the distance from the laundry room to the pool is half the distance from the game room to the shower. c. Turn clockwise 1358 and walk forward 70.7 yards. Geometry Assessment Book
A9
