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