Geometry B
Name ____________________________________
Period _____________________________________
Chapter 5 Review Sheet
Remember these are only a sample set of questions. You are responsible for all of your notes, homework,
and quiz material.
C
1. Given: DB is the perpendicular bisector of AC . Find CB.
B
E
D
12
A
2. Given: EH is an angle bisector of ∠FEG, HF = 5, m∠EFH and m∠EGH = 90°. Find HG.
J
F
E
K
H
G
M
EH bisects
3. Given:
∠JEM, m∠EJK = m∠EMK = 90° and JK = MK =10.
What can you conclude about point K.
J
F
E
K
H
G
M
4. Given: D is the circumcenter of ∆ABC. Find DC. Do you have enough information to find DE? Why
or why not?
B
10
E
F
D
6
A
G
C
Geometry B
F
5. Given: H is the circumcenter of ∆EFG. Find EJ.
15
K
M
H
E
G
J
24
6. Given: Q is the incenter of ∆STR, m∠WQS = 70°. Find m∠QSX. Find QY.
T
W
Y
Q
25
7
S
X
R
7. Given: T is the centroid of ∆ABC, BT = 14, XC = 24, and TZ = 8.5 Find BY, TX, and AT.
C
Y
Z
T
A
B
X
8. Use ∆ABC, where X, Y, and Z are midpoints of the sides. Answer each question. Each question is
separate from one another.
A
CB _______
XY _______
Z
If AB = 8, then YZ = _______
X
If AC = 10, then XY = _______
If XZ = 6, then BC = ________
C
If YZ = 4x – 11 and AB = 3x+3, then YZ = ________
If AZ = 4x – 5 and XY = 2x+1, then AC = _________
Y
B
Geometry B
9. Name the longest and shortest sides of each triangle.
B
E
D
35 °
G
66 °
A
47 °
52°
42°
C
H
95 °
F
J
10. Name the smallest and largest angles of each triangle.
R
12
K
N
L
11
10
8
6
5
Q
M
P
10
5
T
S
7
11. Complete each statement with <,>, or =.
AC __________ EF
A
B
D
m∠1 __________ m∠2
QS __________ TU
Q
E
T
50°
45°
1
2
65°
C
S
R
F
U
m∠1 __________ m∠2
MN __________ PR
P
m∠1 __________ m∠2
15
10
1
M
120°
L
110°
Q
R
N
1
2
2
Geometry B
12. Fill in each blank with sometimes, always, or never. Try drawing a picture.
If P is the circumcenter of ∆RST, then PR, PS, and PS are ____________________ equal.
If BD bisects ∠ABC, then AD & CD are ____________________ congruent.
The incenter of a triangle ____________________ lies outside the triangle.
If R is the centroid of ∆PEU, and T is the midpoint of PU , then ER is ____________________ smaller
than RT .
13. Determine if each statement is true or false. Reminder: in order to be true the statement must always
be true.
____________________ The orthocenter of a right triangle may lie outside the triangle.
____________________ The distance from each vertex of a triangle to its circumcenter is equal.
____________________ A side of a triangle can also be an altitude.
____________________ The orthocenter of a triangle divides a segment in a ratio of 2 to 1.
____________________ The midsegments of a triangle all intersect at a point called the centroid.
Geometry B
In the diagram below, DE , EF , and DF are midsegments.
A
E
B
14. EF ________
15. DF ________
D
F
16. BC ________
17. a. If AB = 22 , then AE = ___________
C
b. If EF = 12 , then AC = ___________
c. If BC = 18 , then DE = ___________
d. Perimeter of ∆ABC = ___________
e. Perimeter of ∆DEF = ___________
f.
If DE = 3 x + 7 and BC = 7 x + 6, then DE = _______________
g. If EF = x + 8 and AC = 20 x − 20, then AC = _______________
Identify each of the following statements as true (T) or false (F).
18. In ∆DEF , if m∠D = 52°, m∠E = 35°, and m∠F = 93°, then DE is the longest side.
_________
19. In ∆XYZ , if XY = 5, YZ = 4, and XZ = 3, then ∠X is the smallest angle.
_________
20. In ∆WED, if m∠W > m∠E > m∠D, then WD > ED > WE
_________
21. 10, 10, and 20 are possible lengths for the sides of a triangle.
_________
22. If the lengths of two sides of a triangle are 7 and 9, then the length of the third side of the
triangle must be greater than 2, but less than 16.
_________
Geometry B
Circle the best answer.
23. In ∆EFG , m∠E = 6 x − 8, m∠F = 7 x + 3, and m∠G = 3 x − 7. The correct order for the sides of
the triangle from shortest to longest is:
a. EG , FE , GF
b. FE , GF , EG
c. EG , GF , FE
d. GF , EG , FE
24. Determine which set of numbers can be the lengths of the sides of a triangle.
a. 3, 7, 4
b. 4, 11, 14
c. 5, 8, 2
25. Two sides of a triangle have lengths 10 cm and 7cm. The length of the third side can be:
a. 2 cm
b. 3 cm
c. 15 cm
d. 17 cm
26. If a triangle has side lengths of 4x, 10 – 2x, and 6x – 8, the possible values for x are:
a. x > 1.5
b. 1.5 < x < 4.5
c. -4.5 < x < 1.5
d. x > 4.5
Complete the statement with the word always, sometimes, or never.
27. The altitude ________________ has a vertex point as an endpoint.
28. The perimeter of the triangle formed by the midsegments is ______________ double that of the
original triangle’s perimeter.
29. The incenter of a triangle ________________ lies outside the triangle.
30. The median of a triangle is ___________________ perpendicular to a side of the triangle.
31. The angle bisectors of an obtuse triangle will _________________ intersect on the triangle.
Geometry B
Fill in the missing word or words for each of the following.
32. The point of intersection of 3 or more lines is called the ________________________________.
33. The point of concurrency of the _________________ of a triangle is called the circumcenter of
the triangle.
34. The point of concurrency of the _________________ of a triangle is called the incenter of the
triangle.
35. The point of concurrency of the _________________ of a triangle is called the centroid of the
triangle.
36. The point of concurrency of the _________________ of a triangle is called the orthocenter of the
triangle.
Given each diagram answer the following questions.
B
37. The largest angle of ∆ABC is ___________.
The smallest angle of ∆ABC is ___________.
14
13
C
A
15
E
38. The largest angle of ∆DEF is ___________.
The smallest angle of ∆DEF is ___________.
7
9
D
F
12
H
39. The largest angle of ∆GHJ is ___________.
The smallest angle of ∆GHJ is ___________.
10
10
G
5
J
Geometry B
40. The longest side of ∆ABC is ___________.
C
The shortest side of ∆ABC is ___________.
80 °
30 °
A
70 °
F
41. The longest side of ∆DEF is ___________.
The shortest side of ∆DEF is ___________.
D
125°
25 °
42. The longest side of ∆GHJ is ___________.
The shortest side of ∆GHJ is ___________.
H
J
44 °
G
A
43. The longest side of ∆ABC is ___________.
x+2
The shortest side of ∆ABC is ___________.
116°
x
B
44. The longest side of ∆DEF is ___________.
C
E
The shortest side of ∆DEF is ___________.
x - 30
x
D
x
110°
F
E
B
Geometry B
Is it possible to have a triangle whose sides have the given lengths?
45.
5, 6, 7
YES
NO
46.
13, 8, 5
YES
NO
47.
4, 10, 5
YES
NO
48.
3, 3, 8
YES
NO
49.
8, 8, 0.1
YES
NO
50.
8, 10, 8
YES
NO
The lengths of two sides of a triangle are given. Determine the range of the possible lengths of the third
side of the triangle.
51.
AB = 5 and BC = 7
The length of AC must be greater than _______ but less than ________ .
52.
AB = 10 and BC = 7
The length of AC must be greater than _______ but less than ________ .
53.
AB = 12 and BC = 12.2
The length of AC must be greater than _______ but less than ________ .
54.
AB = 93 and BC = 1
The length of AC must be greater than _______ but less than ________ .
55.
AB = 6 and BC = 9
The length of AC must be greater than _______ but less than ________ .
56.
AB = 10 and BC = 10
The length of AC must be greater than _______ but less than ________ .