Name ———————————————————————
Standardized Test A
CHAPTER
5
For use after Chapter 5
Multiple Choice
5. In the figure, AP 5 5x and BP 5 3x 1 4. For
1. Every triangle has
?
B exactly 1
C at least 2
D exactly 3
} }
what value of x does P lie on the bisector of aB?
midsegments.
A at least 1
}
2. If BD, DF, and FB are midsegments of
TACE, what is AF?
*
" &
A 2
#
C 20
!
D 30
}
$
If @###$ MN is the perpendicular bisector of RJ, what is RM? " 2
.
. #
B 5
C 6
D 12
? of a triangle is a segment from a vertex to the midpoint of the opposite side.
-
B 9
3
7. A(n)
X
A 8
%
A 4
*
X
D 10
bisectors of TABC. What is NE?
%
B 15
C 6
6. Point N is the intersection of the angle
$
A 10
B 4
C 17
D 19
A median
B midsegment
C altitude
D angle bisector
8. What is AP in the figure below? -
4. In the figure, the perpendicular bisectors of
TBFG meet at point A. What is AF?
3
&
1
!
%
$
"
A 12
96
0
!
#
B 16
Geometry Chapter 5 Assessment Book
A 16 '
C 20
D 22
2
B 18
.
C 24
D 36
Copyright © Holt McDougal. All rights reserved.
!
3.
Date ————————————
Name ——————————————————————— CHAPTER
5
Standardized Test A For use after Chapter 5
continued
Gridded Response
9. What is the shortest side of nXYZ?
} A XY } B XZ } C YZ
:
13. Point Q is the intersection
of the medians of nDEF. What is ME 2 DP?
ª
D cannot be determined
Date ————————————
8 ª
$ 9
-
%
&
Short Response X
C 11
14. In nCRM, CR 5 6 and RM 5 11. Write
inequalities to show all the possible values for CM.
D 18 11. Using the Hinge Theorem, which can be
Extended Response
concluded from the diagram?
15. From a lookout tower, Fire 1 is located
"
9 miles due north and Fire 2 is located 12 miles due east.
%
ª
ª
! # Copyright © Holt McDougal. All rights reserved.
1
B 9
0
10. Which is a possible value of x?
A 7
.
a. Find the shortest distance firefighters
$
&
A AC 5 DE B AC . DF C DF > BC D DF > AC 12. Based on the diagram, which is a true
statement? A m∠ 1 5 m∠ 2
B m∠ 1 < m∠ 2
C m∠ 1 > m∠ 2 } D GK bisects ∠ JGH.
can travel from Fire 1 to Fire 2. Explain. b. A campground is located halfway between the lookout tower and Fire 1, and another campground is located halfway between the lookout tower and Fire 2. Explain how the answer from part (a) can be used to find the distance between the campgrounds. Then find the distance. c. A fire truck is located in the middle of the shortest path between the two fires. It heads towards the campground located between the lookout tower and Fire 2. How far must it travel to reach the campground? Explain.
Geometry Chapter 5 Assessment Book
97
Name ——————————————————————— CHAPTER
5
Date ————————————
Standardized Test B For use after Chapter 5
Multiple Choice
5. Point A is the incenter of nFGH. Find AS.
A 3
1. The segment connecting the midpoints of
two sides of a triangle is parallel to the third side and is ? . A twice as long
B half as long
} } } } }
}
2. If RS, RT, ST, WY, WZ, and YZ are all G
W
Y
T
M
T X
H
C 3
}
B ∠ NZK > ∠ OZK D MK 5 OK
7. The point of concurrency of the three
medians of a triangle is called the ? of the triangle.
R
P (0, 2)
A tri-sector point
B centrino
C median point
D centroid
8. If point P is the centroid of n ABC, find CP.
S (3, 0)
A (6, 1)
x }
}
B Ï 13 C Ï5
5
D }2
4. By the Concurrency of
Perpendicular Bisectors } } Theorem, if QJ, QK, and } QL are perpendicular D bisectors, then ? .
E
B DE 5 EF 5 FD C QD 5 QE 5 QF D ∠ EQK > ∠ FQL > ∠ DQJ Geometry Chapter 5 Assessment Book
C (5, −3)
A 5
J K L F
A ∠ JQK > ∠ KQL > ∠ LQJ
B (10, 1) P
10
5
B } 3
C }3
7
D }3
9. Which is the longest side of nDEF?
} A DE } B DF } C EF
D
D cannot be determined
70°
80° F
E
Copyright © Holt McDougal. All rights reserved.
y
98
Z
O
}
find RS.
3
K
A XK 5 YK } } C NK ⊥ YZ
D 1
3. If QS is the perpendicular bisector of PR,
A }2
H
N
3x
Z
B 2
S 5
Y
6
1 A }2
F
3
which statement can you not conclude?
R
S
C 4
A
6. Given the inscribed circle with center K,
midsegments, find x. F
B 2 D 5
C one third as long D the same length
G
R
Name ———————————————————————
Standardized Test B
CHAPTER
5
Date ————————————
continued
For use after Chapter 5
Gridded Response
10. Which is a possible value of x?
A 2
5
x
nMNP and JP 5 21. Find the perimeter of nMJR.
B 4 8
C 14
13. R is the centroid of
D 17
M
N
R
11. Using the Hinge Theorem and the diagram,
you can conclude:
18
J
9
L
K
P L K
P
120°
60°
Short Response S
M
A m∠ KLM < m∠ QSP
15. A campground has a convenience store
C PS > LM
located 100 yards due south of the shower facilities. There is a game room 100 yards due east of the convenience store.
D none of these 12. Based on the diagram, which is a true
statement? Copyright © Holt McDougal. All rights reserved.
inequality to show all possible values for QR. Extended Response
B QS 5 LM
B 6 A
14. In nPQR, PQ 5 20 and PR 5 9. Write an
E D 5 C
A m∠ A > m∠ D B m∠ A < m∠ D C m∠ A 5 m∠ D } D E is the midpoint of BC.
a. Camper A leaves the game room for
the shower. What is the shortest travel distance possible? b. Camper B is doing laundry half way between the game room and the convenience store. Find the shortest distance Camper B can travel to get to the pool located half way between the store and the shower. c. Camper C is lost, standing at the convenience store facing west. If his tent is equidistant from the store, the shower, and the game room, provide two-step instructions to get Camper C back to the tent.
Geometry Chapter 5 Assessment Book
99
Name ———————————————————————
Date ————————————
Standardized Test C
CHAPTER
5
For use after Chapter 5
5. Point M is the incenter of TXYZ. Find MC.
Multiple Choice 1. Triangle DEF is formed by connecting the
midpoints of TABC. The perimeter of TDEF is 24. What is the perimeter of TABC?
A 12
B 36
C 48
8 X
2. In the diagram, HP 5 x 1 3, MN 5 2x 2 6,
:
"
9
A 12
'
X
! X
D 72
and MP 5 x 1 5. Find GK.
#
B 15
C 31
D 35
6. Which method could have been used to
.
inscribe the circle inside the triangle?
+
#
0
(
A 12
B 14
C 24
D 28
}
!
0
}
1
3. If UW is the perpendicular bisector of TV,
find UV. "
5 4
B Find the incenter P, then use PQ as the radius.
7
C Find the circumcenter P, then use PA as the radius.
6 }
}
}
}
B 3Ï2 C 3Ï5 D Ï 37
A Ï5
D Find the circumcenter P, then use PQ as the radius.
4. Which must be true given that C is the
circumcenter of TGHK?
7. Which statement is not always true?
A The medians of a triangle intersect inside the triangle.
'
2
#
(
B The altitudes of a triangle intersect inside the triangle.
3
4
C A median of a triangle intersects a vertex of the triangle.
+
A CH 5 CK 5 CG B CR 5 CS 5 CT 1
C CH 5 }2 CK
100
Geometry Chapter 5 Assessment Book
2
D CR 5 }3 RK
D An altitude of a triangle intersects a vertex of the triangle.
Copyright © Holt McDougal. All rights reserved.
A Find the incenter P, then use PA as the radius.
Name ——————————————————————— CHAPTER
5
Standardized Test C For use after Chapter 5
8. Given that P is the centroid of TABC,
continued
Gridded Response
find PD.
Date ————————————
13. Point A is the centroid of
TDEF. Find the perimeter of TADN.
! # $
0
$
.
"
10
A } 3
20
B } 3
&
C 5
0
%
D 10
9. In TPTR, m∠ P 5 55° and m∠ R 5 45°.
Which list gives the sides in order from shortest to longest? } } } } } } B RT, PT, PR A PR, RT, PT } } } } } } C PT, PR, RT D PT, RT, PR
Short Response 14. In nSTR, ST 5 23.6 and TR 5 31.5. Write
an inequality to show all the possible values for SR.
10. Which can be the measures of the sides of
a triangle?
Extended Response 15. A cargo ship travels due north from a port
B 4 cm, 6 cm, 8 cm
at a rate of 15 miles per hour while a cruise ship leaves the port at the same time, traveling due east at 20 miles per hour.
C 5 cm, 5 cm, 12 cm
a. Both ships stop after three hours.
D 6 cm, 7 cm, 15 cm
What is the shortest distance between the ships? Explain. b. There is an island 45 miles due north of the cargo ship and another island 60 miles due east of the cruise ship. Explain how the answer from part (a) can be used to find the shortest distance between the islands. c. A sailboat is equidistant from the two islands and the port. What is the shortest distance between the sailboat and the cargo ship? the sailboat and the port? the sailboat and the cruise ship?
A 3 cm, 4 cm, 7 cm
Copyright © Holt McDougal. All rights reserved.
!
}
11. Given that L is the midpoint of JN, which
can be concluded from the diagram? A KL , ML B KL . ML
*
-
ª
C KL 5 ML ,
D KL , LN
ª +
.
12. By the Hinge Theorem, which inequality
gives the correct restriction on x? A x,3
X X
B x.3 C x,9 D x.9
ª
ª
Geometry Chapter 5 Assessment Book
101
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
Chapter 5, continued
1. C 2. D 3. C 4. A 5. C 6. B 7. B 8. A
ANSWERS
9. D 10. B 11. A 12. B 13. 28.45 14. 7.9 , x , 55.1
Quiz 3 1. 27 2. 20 3. 42 4.
}
is Ï 452 1 602 5 75 miles. b. The islands and the port form a triangle where the ships’ current locations are midpoints of two sides, making the shortest path between the ships a midsegment of the triangle. The shortest distance between the islands is parallel to this side and twice as long, so the distance is 150 miles. c. 60 miles; 75 miles; 45 miles 1. A 2. B 3. E 4. C 5. D 6. A 7. D 8. A 9. B 10. C 11. E 12. 18 13. 41
Performance Assessment 1. Complete answers should include: an explanation that a coordinate proof involves placing geometric figures in a coordinate plane; an explanation that when variables are used to represent the coordinates of a figure in a coordinate proof, the results are true for all figures of the given type; an example of a coordinate proof; an explanation that an indirect proof involves the assumption that the desired conclusion is false and that this original assumption must be shown to be impossible; an example of an indirect proof. 2. a. (65, 50) and (100, 50) b. 35 units c. No. Because the triangle is obtuse, the circumcenter will lie outside of the rose garden. d. about (70, 30) e. about (20, 110) f. about (177, 110) g. The length of the third side must be less than 7 feet and greater than 1 foot.
Chapter 6 Quiz 1 9 1. x 5 6 2. s 5 15 3. a 5 10 4. } 7 y17 2 8 5. } or } 6. } 7. 11.2 7 3 12
Quiz 2 1. 2 : 1 2. 18 3. 28 4. 122 5. 164, 82 6. 1, 2, 3, 5
3 5 2 7. } 5 2, } 5 1.5, } ø 1.667 1 2 3
8. similar; n ABC , nDEF 9. not similar
Geometry Assessment Book
y
5.
y
15. a. By the Pythagorean Theorem, the distance
SAT/ACT Chapter Test
A10
10. similar; nPQR , nTSR
22
x
2
1 1
x
Chapter Test A 17 8 40 4 1. } 2. } 3. } 4. } 5. x 5 24 2 1 1 1
6. x 5 14 }
7. x 5 1 8. x 5 5 9. 12 10. 20 11. 6Ï 10
2 12. 15 13. 18 14. similar; JKLM , PQRS, } 5 4 15. similar; nTUV , nXYZ, } 3 16. similar; n ABC , nGFH 17. not similar 18. not similar 19. similar; nDHG , nFHE 20. x 5 12 21. x 5 24 22. x 5 28 23. x 5 26
1 24. 3 25. } 10 26. length 5 140 m, width 5 80 m
Chapter Test B 20 528 9 3 1. 5 : 1 2. } 3. } 4. } 5. 30 : 1 6. } 1 1 1 1 7. 4.5 8. 5 9. 5 10. 24 11. n ABD , nECD; AA Similarity Postulate 12. no 13. 22.5 14. 95 15. 1.5 16. 12 1 17. 2 18. } 12 19. 8 in., 4 in. 20. 26 in., 6.5 in. 21. 5 ft
Chapter Test C 4 1 24 1. } 2. } 3. } 4. x 5 14 5. x 5 24 5 9 1 39 320 8 6. x 5 7 7. } 8. } 9. 4 m 10. } 5 5 31 1 11. 11 } 12. LM 5 8.1, PQ 5 13.0 5 13. 55, 89, 144, 233
89 233 144 14. } ø 1.6182, } ø 1.6179, } ø 1.6181 55 89 144 15. similar; n ABE , nCBD 16. not similar 17. similar; nJKL , nJMN 18. similar; nEHD , nGHF 19. x 5 16 20. x 5 7
Copyright © Holt McDougal. All rights reserved.
Standardized Test C
