Download Geometry - Chapter 5 Review

Name: ________________________ Class: ___________________ Date: __________
ID: A
Geometry - Chapter 5 Review
1. Points B, D, and F are midpoints of the sides of
ACE. EC = 30 and DF = 17. Find AC.
The diagram is not to scale.
3. Find the value of x. The diagram is not to scale.
A.
B.
C.
D.
A.
B.
C.
D.
60
30
34
8.5
90
70
35
48
4. Use the information in the diagram to determine the
height of the tree. The diagram is not to scale.
2. Find the value of x.
A.
B.
C.
D.
A.
B.
C.
D.
7
11.5
8
10
1
75 ft
150 ft
35.5 ft
37.5 ft
Name: ________________________
ID: A
5. Use the information in the diagram to determine the measure of the angle x formed by the line from the point on the
ground to the top of the building and the side of the building. The diagram is not to scale.
A. 52
B. 26
C. 104
6. A triangular side of the Transamerica Pyramid
Building in San Francisco, California, is 149 feet at
its base. If the distance from a base corner of the
building to its peak is 859 feet, how wide is the
triangle halfway to the top?
D. 38
7. The length of DE is shown. What other length can
you determine for this diagram?
A.
B.
C.
D.
A.
B.
C.
D.
298 ft
74.5 ft
149 ft
429.5 ft
2
DF = 12
EF = 6
DG = 6
No other length can be determined.
Name: ________________________
ID: A
10. Q is equidistant from the sides of TSR. Find
mRST. The diagram is not to scale.
8. Which statement can you conclude is true from the
given information?



Given: AB is the perpendicular bisector of IK .
A.
B.
C.
D.
AJ = BJ
IAJ is a right angle.
IJ = JK
A is the midpoint of IK .
A.
B.
C.
D.


21
42
4
8
11. Q is equidistant from the sides of TSR. Find the
value of x. The diagram is not to scale.
9. DF bisects EDG. Find the value of x. The
diagram is not to scale.
A. 285
4
B.
19
C. 32
D. 19
A.
B.
C.
D.
3
2
12
14
24
Name: ________________________
ID: A
12. Which diagram shows a point P an equal distance
from points A, B, and C?
A.
13. Where can the perpendicular bisectors of the sides
of a right triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
A. I only
B. II only
C. I or II only
D. I, II, or II
B.
C.
D.
4
Name: ________________________
ID: A
14. Name the point of concurrency of the angle bisectors.
A. A
B. B
C. C
16. In ACE, G is the centroid and BE = 18. Find BG
and GE.
15. Find the length of AB, given that DB is a median of
the triangle and AC = 26.
A.
B.
C.
D.
D. not shown
A. BG  6, GE  12
B. BG  12, GE  6
1
1
C. BG = 4 , GE = 13
2
2
D. BG = 9, GE = 9
13
26
52
not enough information
17. In ABC, centroid D is on median AM . AD  x  4
and DM  2x  4. Find AM.
A. 13
B. 4
C. 12
D. 6
5
Name: ________________________
ID: A
18. Name a median for ABC.
A.
B.
C.
D.
21. Which labeled angle has the greatest measure? The
diagram is not to scale.
AD
CE
AF
BD
A.
B.
C.
D.
19. Where can the medians of a triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
A. I only
B. III only
C. I or III only
D. I, II, or II
1
2
3
not enough information in the diagram
22. Name the smallest angle of ABC. The diagram is
not to scale.
20. For a triangle, list the respective names of the points
of concurrency of
• perpendicular bisectors of the sides
• bisectors of the angles
• medians
• lines containing the altitudes
A. incenter
circumcenter
centroid
orthocenter
B. circumcenter
incenter
centroid
orthocenter
C. circumcenter
incenter
orthocenter
centroid
D. incenter
circumcenter
orthocenter
centroid
A.
B.
C.
D.
A
B
C
Two angles are the same size and smaller than
the third.
23. Three security cameras were mounted at the corners
of a triangular parking lot. Camera 1 was 156 ft
from camera 2, which was 101 ft from camera 3.
Cameras 1 and 3 were 130 ft apart. Which camera
had to cover the greatest angle?
A. camera 2
B. camera 1
C. camera 3
D. cannot tell
6
Name: ________________________
ID: A
24. Name the second largest of the four angles named in
the figure (not drawn to scale) if the side included by
1 and 2 is 11 cm, the side included by 2 and
3 is 16 cm, and the side included by 3 and 1 is
14 cm.
27. Which three lengths CANNOT be the lengths of the
sides of a triangle?
A. 23 m, 17 m, 14 m
B. 11 m, 11 m, 12 m
C. 5 m, 7 m, 8 m
D. 21 m, 6 m, 10 m
28. Which three lengths could be the lengths of the sides
of a triangle?
A. 12 cm, 5 cm, 17 cm
B. 10 cm, 15 cm, 24 cm
C. 9 cm, 22 cm, 11 cm
D. 21 cm, 7 cm, 6 cm
A.
B.
C.
D.
29. Two sides of a triangle have lengths 6 and 17.
Which expression describes the length of the third
side?
A. at least 11 and less than 23
B. at least 11 and at most 23
C. greater than 11 and at most 23
D. greater than 11 and less than 23
3
4
2
1
25. mA  9x  7, mB  7x  9, and mC  28  2x.
List the sides of ABC in order from shortest to
longest.
A. AB; AC; BC
B. BC ; AB; AC
C. AC; AB; BC
D. AB; BC ; AC
30. Two sides of a triangle have lengths 5 and 12.
Which inequalities represent the possible lengths for
the third side, x?
A. 5  x  12
B. 7  x  5
C. 7  x  17
D. 7  x  12
26. List the sides in order from shortest to longest. The
diagram is not to scale.
A.
B.
C.
D.
JK , LJ , LK
LK , LJ , JK
JK , LK , LJ
LK , JK , LJ
7
Name: ________________________
ID: A
31. Which of the following must be true?
The diagram is not to scale.
A.
B.
C.
D.
33. What is the range of possible values for x?
The diagram is not to scale.
AB  BC
AC  FH
BC  FH
AC  FH
A.
B.
C.
D.
32. If mDBC  73, what is the relationship between
AD and CD?
A.
B.
C.
D.
0  x  54
0  x  108
0  x  27
27  x  180
34. What is the range of possible values for x?
The diagram is not to scale.
AD  CD
AD  CD
AD  CD
not enough information
A.
B.
C.
D.
8
12  x  48
0  x  10
10  x  50
10  x  43
Name: ________________________
ID: A
35. Identify parallel segments in the diagram.
9
ID: A
Geometry - Chapter 5 Review
Answer Section
1. ANS:
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C
PTS: 1
DIF: L3
REF: 5-1 Midsegments of Triangles
5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c
5-1 Problem 2 Finding Lengths
KEY: midpoint | midsegment | Triangle Midsegment Theorem
C
PTS: 1
DIF: L3
REF: 5-1 Midsegments of Triangles
5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c
5-1 Problem 2 Finding Lengths
KEY: midpoint | midsegment | Triangle Midsegment Theorem
B
PTS: 1
DIF: L3
REF: 5-1 Midsegments of Triangles
5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c
5-1 Problem 2 Finding Lengths
KEY: midsegment | Triangle Midsegment Theorem
A
PTS: 1
DIF: L3
REF: 5-1 Midsegments of Triangles
5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c
5-1 Problem 3 Using a Midsegment of a Triangle
midsegment | Triangle Midsegment Theorem | problem solving
A
PTS: 1
DIF: L3
REF: 5-1 Midsegments of Triangles
5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c
5-1 Problem 3 Using a Midsegment of a Triangle
midsegment | Triangle Midsegment Theorem | problem solving
B
PTS: 1
DIF: L3
REF: 5-1 Midsegments of Triangles
5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c
5-1 Problem 3 Using a Midsegment of a Triangle
midsegment | Triangle Midsegment Theorem | word problem | problem solving
B
PTS: 1
DIF: L3
REF: 5-2 Perpendicular and Angle Bisectors
5-2.1 To use properties of perpendicular bisectors and angle bisectors
CC G.CO.9| CC G.CO.12| CC G.SRT.5| G.3.c
5-2 Problem 1 Using the Perpendicular Bisector Theorem
equidistant | perpendicular bisector | Perpendicular Bisector Theorem
C
PTS: 1
DIF: L3
REF: 5-2 Perpendicular and Angle Bisectors
5-2.1 To use properties of perpendicular bisectors and angle bisectors
CC G.CO.9| CC G.CO.12| CC G.SRT.5| G.3.c
5-2 Problem 1 Using the Perpendicular Bisector Theorem
equidistant | perpendicular bisector | Perpendicular Bisector Theorem | reasoning
D
PTS: 1
DIF: L3
REF: 5-2 Perpendicular and Angle Bisectors
5-2.1 To use properties of perpendicular bisectors and angle bisectors
CC G.CO.9| CC G.CO.12| CC G.SRT.5| G.3.c
5-2 Problem 3 Using the Angle Bisector Theorem
KEY: Angle Bisector Theorem | angle bisector
B
PTS: 1
DIF: L3
REF: 5-2 Perpendicular and Angle Bisectors
5-2.1 To use properties of perpendicular bisectors and angle bisectors
CC G.CO.9| CC G.CO.12| CC G.SRT.5| G.3.c
5-2 Problem 3 Using the Angle Bisector Theorem
Converse of the Angle Bisector Theorem | angle bisector
1
ID: A
11. ANS: A
PTS: 1
DIF: L2
REF: 5-2 Perpendicular and Angle Bisectors
OBJ: 5-2.1 To use properties of perpendicular bisectors and angle bisectors
NAT: CC G.CO.9| CC G.CO.12| CC G.SRT.5| G.3.c
TOP: 5-2 Problem 3 Using the Angle Bisector Theorem
KEY: angle bisector | Converse of the Angle Bisector Theorem
12. ANS: A
PTS: 1
DIF: L2
REF: 5-3 Bisectors in Triangles
OBJ: 5-3.1 To identify properties of perpendicular bisectors and angle bisectors
NAT: CC G.C.3| G.3.c
TOP: 5-3 Problem 1 Finding the Circumcenter of a Triangle
KEY: circumcenter of the triangle | circumscribe | point of concurrency
13. ANS: B
PTS: 1
DIF: L4
REF: 5-3 Bisectors in Triangles
OBJ: 5-3.1 To identify properties of perpendicular bisectors and angle bisectors
NAT: CC G.C.3| G.3.c
TOP: 5-3 Problem 1 Finding the Circumcenter of a Triangle
KEY: circumcenter of the triangle | perpendicular bisector | reasoning | right triangle
14. ANS: C
PTS: 1
DIF: L3
REF: 5-3 Bisectors in Triangles
OBJ: 5-3.1 To identify properties of perpendicular bisectors and angle bisectors
NAT: CC G.C.3| G.3.c
TOP: 5-3 Problem 3 Identifying and Using the Incenter of a Triangle
KEY: angle bisector | incenter of the triangle | point of concurrency
15. ANS: A
PTS: 1
DIF: L2
REF: 5-4 Medians and Altitudes
OBJ: 5-4.1 To identify properties of medians and altitudes of a triangle
NAT: CC G.CO.10| G.3.c
TOP: 5-4 Problem 1 Finding the Length of a Median
KEY: median of a triangle
16. ANS: A
PTS: 1
DIF: L3
REF: 5-4 Medians and Altitudes
OBJ: 5-4.1 To identify properties of medians and altitudes of a triangle
NAT: CC G.CO.10| G.3.c
TOP: 5-4 Problem 1 Finding the Length of a Median
KEY: centroid of a triangle | median of a triangle
17. ANS: C
PTS: 1
DIF: L4
REF: 5-4 Medians and Altitudes
OBJ: 5-4.1 To identify properties of medians and altitudes of a triangle
NAT: CC G.CO.10| G.3.c
TOP: 5-4 Problem 1 Finding the Length of a Median
KEY: centroid of a triangle | median of a triangle
18. ANS: D
PTS: 1
DIF: L3
REF: 5-4 Medians and Altitudes
OBJ: 5-4.1 To identify properties of medians and altitudes of a triangle
NAT: CC G.CO.10| G.3.c
TOP: 5-4 Problem 2 Identifying Medians and Altitudes
KEY: median of a triangle
19. ANS: A
PTS: 1
DIF: L3
REF: 5-4 Medians and Altitudes
OBJ: 5-4.1 To identify properties of medians and altitudes of a triangle
NAT: CC G.CO.10| G.3.c
TOP: 5-4 Problem 2 Identifying Medians and Altitudes
KEY: median of a triangle | centroid of a triangle | reasoning
20. ANS: B
PTS: 1
DIF: L3
REF: 5-4 Medians and Altitudes
OBJ: 5-4.1 To identify properties of medians and altitudes of a triangle
NAT: CC G.CO.10| G.3.c
TOP: 5-4 Problem 3 Finding the Orthocenter
KEY: angle bisector | circumcenter of the triangle | centroid of a triangle | orthocenter of the triangle | median |
altitude of a triangle | perpendicular bisector
21. ANS: C
PTS: 1
DIF: L2
REF: 5-6 Inequalities in One Triangle
OBJ: 5-6.1 To use inequalities involving angles and sides of triangles
NAT: CC G.CO.10| G.3.c
TOP: 5-6 Problem 1 Applying the Corollary
KEY: corollary to the Triangle Exterior Angle Theorem
2
ID: A
22. ANS:
OBJ:
NAT:
23. ANS:
OBJ:
NAT:
KEY:
24. ANS:
OBJ:
NAT:
KEY:
25. ANS:
OBJ:
NAT:
KEY:
26. ANS:
OBJ:
NAT:
27. ANS:
OBJ:
NAT:
KEY:
28. ANS:
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NAT:
KEY:
29. ANS:
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KEY:
30. ANS:
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KEY:
31. ANS:
OBJ:
TOP:
32. ANS:
OBJ:
TOP:
33. ANS:
OBJ:
TOP:
34. ANS:
OBJ:
TOP:
B
PTS: 1
DIF: L3
REF: 5-6 Inequalities in One Triangle
5-6.1 To use inequalities involving angles and sides of triangles
CC G.CO.10| G.3.c
TOP: 5-6 Problem 2 Using Theorem 5-10
C
PTS: 1
DIF: L3
REF: 5-6 Inequalities in One Triangle
5-6.1 To use inequalities involving angles and sides of triangles
CC G.CO.10| G.3.c
TOP: 5-6 Problem 2 Using Theorem 5-10
word problem | problem solving
D
PTS: 1
DIF: L4
REF: 5-6 Inequalities in One Triangle
5-6.1 To use inequalities involving angles and sides of triangles
CC G.CO.10| G.3.c
TOP: 5-6 Problem 2 Using Theorem 5-10
corollary to the Triangle Exterior Angle Theorem
A
PTS: 1
DIF: L4
REF: 5-6 Inequalities in One Triangle
5-6.1 To use inequalities involving angles and sides of triangles
CC G.CO.10| G.3.c
TOP: 5-6 Problem 3 Using Theorem 5-11
multi-part question
B
PTS: 1
DIF: L3
REF: 5-6 Inequalities in One Triangle
5-6.1 To use inequalities involving angles and sides of triangles
CC G.CO.10| G.3.c
TOP: 5-6 Problem 3 Using Theorem 5-11
D
PTS: 1
DIF: L3
REF: 5-6 Inequalities in One Triangle
5-6.1 To use inequalities involving angles and sides of triangles
CC G.CO.10| G.3.c
TOP: 5-6 Problem 4 Using the Triangle Inequality Theorem
Triangle Inequality Theorem
B
PTS: 1
DIF: L3
REF: 5-6 Inequalities in One Triangle
5-6.1 To use inequalities involving angles and sides of triangles
CC G.CO.10| G.3.c
TOP: 5-6 Problem 4 Using the Triangle Inequality Theorem
Triangle Inequality Theorem
D
PTS: 1
DIF: L3
REF: 5-6 Inequalities in One Triangle
5-6.1 To use inequalities involving angles and sides of triangles
CC G.CO.10| G.3.c
TOP: 5-6 Problem 5 Finding Possible Side Lengths
Triangle Inequality Theorem
C
PTS: 1
DIF: L3
REF: 5-6 Inequalities in One Triangle
5-6.1 To use inequalities involving angles and sides of triangles
CC G.CO.10| G.3.c
TOP: 5-6 Problem 5 Finding Possible Side Lengths
Triangle Inequality Theorem
D
PTS: 1
DIF: L3
REF: 5-7 Inequalities in Two Triangles
5-7.1 To apply inequalities in two triangles
NAT: CC G.CO.10| G.3.c
5-7 Problem 1 Using the Hinge Theorem
C
PTS: 1
DIF: L3
REF: 5-7 Inequalities in Two Triangles
5-7.1 To apply inequalities in two triangles
NAT: CC G.CO.10| G.3.c
5-7 Problem 1 Using the Hinge Theorem
C
PTS: 1
DIF: L2
REF: 5-7 Inequalities in Two Triangles
5-7.1 To apply inequalities in two triangles
NAT: CC G.CO.10| G.3.c
5-7 Problem 3 Using the Converse of the Hinge Theorem
D
PTS: 1
DIF: L3
REF: 5-7 Inequalities in Two Triangles
5-7.1 To apply inequalities in two triangles
NAT: CC G.CO.10| G.3.c
5-7 Problem 3 Using the Converse of the Hinge Theorem
3
ID: A
35. ANS:
BD  AE, DF  AC, BF  CE
PTS:
OBJ:
TOP:
KEY:
1
DIF: L2
REF: 5-1 Midsegments of Triangles
5-1.1 To use properties of midsegments to solve problems NAT: CC G.CO.10| CC G.SRT.5| G.3.c
5-1 Problem 1 Identifying Parallel Segments
midsegment | parallel lines | Triangle Midsegment Theorem
4