Name: ________________________ Class: ___________________ Date: __________
ID: A
Ch 5 Practice Exam
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Find the value of x. The diagram is not to scale.
a.
____
32
b.
50
c.
64
d.
80
2. B is the midpoint of AC, D is the midpoint of CE, and AE = 11. Find BD. The diagram is not to scale.
a.
5.5
b.
11
c.
1
22
d.
4.5
Name: ________________________
____
3. Points B, D, and F are midpoints of the sides of ∆ACE. EC = 35 and DF = 23. Find AC. The diagram is not to
scale.
a.
____
70
b.
46
c.
11.5
d.
35
b.
5
c.
8.5
d.
8
d.
37
4. Find the value of x.
a.
____
ID: A
6
5. Find the length of the midsegment. The diagram is not to scale.
a.
22.6
b.
88
c.
2
44
Name: ________________________
____
6. Q is equidistant from the sides of ∠TSR. Find the value of x. The diagram is not to scale.
a.
____
27
b.
3
c.
15
d.
30
d.
6
7. DF bisects ∠EDG. Find the value of x. The diagram is not to scale.
a.
____
ID: A
23
42
b.
90
c.
30
8. Which statement can you conclude is true from the given information?
←

→
Given: AB is the perpendicular bisector of IK.
a.
b.
AJ = BJ
∠IAJ is a right angle.
c.
d.
3
IJ = JK
A is the midpoint of IK .
Name: ________________________
____
ID: A
9. Find the center of the circle that you can circumscribe about the triangle.
a.
1
(− , –4)
2
b.
(–3, −2)
c.
1
(− , −2)
2
d.
1
(−2, − )
2
____ 10. Find the center of the circle that you can circumscribe about ∆EFG with E(4, 4), F(4, 2), and G(8, 2).
a. (6, 3)
b. (4, 2)
c. (4, 4)
d. (3, 6)
____ 11. Where can the bisectors of the angles of an obtuse 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
____ 12. In ∆ACE, G is the centroid and BE = 12. Find BG and GE.
a.
b.
BG = 4, GE = 8
BG = 3, GE = 9
c.
d.
4
BG = 8, GE = 4
BG = 6, GE = 6
d.
I, II, or II
Name: ________________________
ID: A
____ 13. Name a median for ∆PQR.
a.
PU
b.
RT
c.
PS
d.
QS
d.
not shown
____ 14. Name the point of concurrency of the angle bisectors.
a.
A
b.
B
c.
C
____ 15. Find the length of AB, given that DB is a median of the triangle and AC = 30.
a.
b.
15
30
c.
d.
____ 16. 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.
5
60
not enough information
I or III only
d.
I, II, or II
Name: ________________________
ID: A
____ 17. What is the name of the segment inside the large triangle?
a.
b.
median
angle bisector
c.
d.
midsegment
perpendicular bisector
____ 18. What is the name of the segment inside the large triangle?
a.
b.
perpendicular bisector
median
c.
d.
altitude
midsegment
____ 19. In ∆ABC, centroid D is on median AM . AD = x + 6 and DM = 2x − 3. Find AM.
1
a. 15
b. 16
c. 4
d. 7
2
____ 20. What is the inverse of this statement?
If she studies hard in math, she will succeed.
a. If she will succeed, then she does not study hard in math.
b. If she studies hard in math, she will not succeed.
c. If she does not study hard in math, she will not succeed.
d. If she does not study hard in math, she will succeed.
____ 21. What is the contrapositive of this statement?
If a figure has three sides, it is a triangle.
a. If a figure does not have three sides, it is a triangle.
b. If a figure is not a triangle, then it does not have three sides.
c. If a figure has three sides, it is not a triangle.
d. If a figure is a triangle, then it does not have three sides.
6
Name: ________________________
ID: A
____ 22. Name the smallest angle of ∆ABC. The diagram is not to scale.
a.
b.
c.
d.
∠A
Two angles are the same size and smaller than the third.
∠B
∠C
____ 23. List the sides in order from shortest to longest. The diagram is not to scale.
a.
LJ, LK, JK
b.
LJ, JK, LK
c.
JK, LJ, LK
d.
JK, LK, LJ
____ 24. Which three lengths could be the lengths of the sides of a triangle?
a. 19 cm, 6 cm, 7 cm
c. 7 cm, 24 cm, 12 cm
b. 10 cm, 13 cm, 22 cm
d. 13 cm, 5 cm, 18 cm
____ 25. Two sides of a triangle have lengths 10 and 18. Which inequalities describe the values that possible lengths
for the third side?
a. x ≥ 8 and x ≤ 28
c. x > 10 and x < 18
b. x > 8 and x < 28
d. x ≥ 10 and x ≤ 18
____ 26. Two sides of a triangle have lengths 9 and 16. What must be true about the length of the third side, x?
a. 7 < x < 16
b. 9 < x < 16
c. 7 < x < 25
d. 7 < x < 9
____ 27. m∠A = 10x − 5, m∠B = 5x − 10, and m∠C = 52 − 2x. List the sides of ∆ABC in order from shortest to longest.
a. AB; BC; AC
b. AC; AB; BC
c. AB; AC; BC
d. BC; AB; AC
Short Answer
28. To prove “p is equal to q” using an indirect proof, what would your starting assumption be?
7
ID: A
Ch 5 Practice Exam
Answer Section
MULTIPLE CHOICE
1. ANS:
OBJ:
TOP:
2. ANS:
OBJ:
TOP:
3. ANS:
OBJ:
TOP:
4. ANS:
OBJ:
KEY:
5. ANS:
OBJ:
KEY:
6. ANS:
OBJ:
STA:
KEY:
7. ANS:
OBJ:
STA:
KEY:
8. ANS:
OBJ:
STA:
KEY:
9. ANS:
REF:
STA:
KEY:
10. ANS:
REF:
STA:
KEY:
11. ANS:
REF:
STA:
12. ANS:
REF:
STA:
KEY:
C
PTS: 1
DIF: L2
REF: 5-1 Midsegments of Triangles
5-1.1 Using Properties of Midsegments
STA: CA GEOM 17.0
5-1 Example 1
KEY: midsegment | Triangle Midsegment Theorem
A
PTS: 1
DIF: L2
REF: 5-1 Midsegments of Triangles
5-1.1 Using Properties of Midsegments
STA: CA GEOM 17.0
5-1 Example 1
KEY: midpoint | midsegment | Triangle Midsegment Theorem
B
PTS: 1
DIF: L2
REF: 5-1 Midsegments of Triangles
5-1.1 Using Properties of Midsegments
STA: CA GEOM 17.0
5-1 Example 1
KEY: midpoint | midsegment | Triangle Midsegment Theorem
A
PTS: 1
DIF: L3
REF: 5-1 Midsegments of Triangles
5-1.1 Using Properties of Midsegments
STA: CA GEOM 17.0
midpoint | midsegment | Triangle Midsegment Theorem
C
PTS: 1
DIF: L3
REF: 5-1 Midsegments of Triangles
5-1.1 Using Properties of Midsegments
STA: CA GEOM 17.0
midsegment | Triangle Midsegment Theorem
B
PTS: 1
DIF: L2
REF: 5-2 Bisectors in Triangles
5-2.1 Perpendicular Bisectors and Angle Bisectors
CA GEOM 2.0| CA GEOM 4.0| CA GEOM 5.0
TOP: 5-2 Example 2
angle bisector | Converse of the Angle Bisector Theorem
D
PTS: 1
DIF: L2
REF: 5-2 Bisectors in Triangles
5-2.1 Perpendicular Bisectors and Angle Bisectors
CA GEOM 2.0| CA GEOM 4.0| CA GEOM 5.0
TOP: 5-2 Example 2
Angle Bisector Theorem | angle bisector
C
PTS: 1
DIF: L3
REF: 5-2 Bisectors in Triangles
5-2.1 Perpendicular Bisectors and Angle Bisectors
CA GEOM 2.0| CA GEOM 4.0| CA GEOM 5.0
perpendicular bisector | Perpendicular Bisector Theorem | reasoning
C
PTS: 1
DIF: L2
5-3 Concurrent Lines, Medians, and Altitudes
OBJ: 5-3.1 Properties of Bisectors
CA GEOM 2.0| CA GEOM 21.0
TOP: 5-3 Example 1
circumscribe | circumcenter of the triangle
A
PTS: 1
DIF: L2
5-3 Concurrent Lines, Medians, and Altitudes
OBJ: 5-3.1 Properties of Bisectors
CA GEOM 2.0| CA GEOM 21.0
TOP: 5-3 Example 1
circumcenter of the triangle | circumscribe
A
PTS: 1
DIF: L3
5-3 Concurrent Lines, Medians, and Altitudes
OBJ: 5-3.1 Properties of Bisectors
CA GEOM 2.0| CA GEOM 21.0
KEY: incenter of the triangle | angle bisector | reasoning
A
PTS: 1
DIF: L2
5-3 Concurrent Lines, Medians, and Altitudes
OBJ: 5-3.2 Medians and Altitudes
CA GEOM 2.0| CA GEOM 21.0
TOP: 5-3 Example 3
centroid | median of a triangle
1
ID: A
13. ANS:
REF:
STA:
KEY:
14. ANS:
REF:
STA:
KEY:
15. ANS:
REF:
STA:
KEY:
16. ANS:
REF:
STA:
17. ANS:
REF:
STA:
KEY:
18. ANS:
REF:
STA:
KEY:
19. ANS:
REF:
STA:
20. ANS:
REF:
OBJ:
TOP:
21. ANS:
REF:
OBJ:
TOP:
22. ANS:
OBJ:
TOP:
23. ANS:
OBJ:
TOP:
24. ANS:
OBJ:
TOP:
25. ANS:
OBJ:
TOP:
D
PTS: 1
DIF: L2
5-3 Concurrent Lines, Medians, and Altitudes
OBJ: 5-3.2 Medians and Altitudes
CA GEOM 2.0| CA GEOM 21.0
TOP: 5-3 Example 4
median of a triangle
C
PTS: 1
DIF: L2
5-3 Concurrent Lines, Medians, and Altitudes
OBJ: 5-3.2 Medians and Altitudes
CA GEOM 2.0| CA GEOM 21.0
angle bisector | incenter of the triangle | point of concurrency
A
PTS: 1
DIF: L2
5-3 Concurrent Lines, Medians, and Altitudes
OBJ: 5-3.2 Medians and Altitudes
CA GEOM 2.0| CA GEOM 21.0
TOP: 5-3 Example 3
median of a triangle
A
PTS: 1
DIF: L3
5-3 Concurrent Lines, Medians, and Altitudes
OBJ: 5-3.2 Medians and Altitudes
CA GEOM 2.0| CA GEOM 21.0
KEY: median of a triangle | centroid | reasoning
B
PTS: 1
DIF: L2
5-3 Concurrent Lines, Medians, and Altitudes
OBJ: 5-3.2 Medians and Altitudes
CA GEOM 2.0| CA GEOM 21.0
TOP: 5-3 Example 4
altitude of a triangle | angle bisector | perpendicular bisector | midsegment | median of a triangle
A
PTS: 1
DIF: L2
5-3 Concurrent Lines, Medians, and Altitudes
OBJ: 5-3.2 Medians and Altitudes
CA GEOM 2.0| CA GEOM 21.0
TOP: 5-3 Example 4
altitude of a triangle | angle bisector | perpendicular bisector | midsegment | median of a triangle
A
PTS: 1
DIF: L3
5-3 Concurrent Lines, Medians, and Altitudes
OBJ: 5-3.2 Medians and Altitudes
CA GEOM 2.0| CA GEOM 21.0
KEY: centroid | median of a triangle
C
PTS: 1
DIF: L2
5-4 Inverses, Contrapositives, and Indirect Reasoning
5-4.1 Writing the Negation, Inverse, and Contrapositive STA: CA GEOM 2.0
5-4 Example 2
KEY: contrapositive
B
PTS: 1
DIF: L2
5-4 Inverses, Contrapositives, and Indirect Reasoning
5-4.1 Writing the Negation, Inverse, and Contrapositive STA: CA GEOM 2.0
5-4 Example 2
KEY: contrapositive
C
PTS: 1
DIF: L2
REF: 5-5 Inequalities in Triangles
5-5.1 Inequalities Involving Angles of Triangles
STA: CA GEOM 2.0| CA GEOM 6.0
5-5 Example 2
KEY: Theorem 5-10
D
PTS: 1
DIF: L2
REF: 5-5 Inequalities in Triangles
5-5.2 Inequalities Involving Sides of Triangles
STA: CA GEOM 2.0| CA GEOM 6.0
5-5 Example 3
KEY: Theorem 5-11
B
PTS: 1
DIF: L2
REF: 5-5 Inequalities in Triangles
5-5.2 Inequalities Involving Sides of Triangles
STA: CA GEOM 2.0| CA GEOM 6.0
5-5 Example 4
KEY: Triangle Inequality Theorem
B
PTS: 1
DIF: L2
REF: 5-5 Inequalities in Triangles
5-5.2 Inequalities Involving Sides of Triangles
STA: CA GEOM 2.0| CA GEOM 6.0
5-5 Example 5
KEY: Triangle Inequality Theorem
2
ID: A
26. ANS:
OBJ:
TOP:
27. ANS:
OBJ:
KEY:
C
PTS: 1
DIF: L2
REF: 5-5 Inequalities in Triangles
5-5.2 Inequalities Involving Sides of Triangles
STA: CA GEOM 2.0| CA GEOM 6.0
5-5 Example 5
KEY: Triangle Inequality Theorem
C
PTS: 1
DIF: L4
REF: 5-5 Inequalities in Triangles
5-5.2 Inequalities Involving Sides of Triangles
STA: CA GEOM 2.0| CA GEOM 6.0
Theorem 5-11 | multi-part question
SHORT ANSWER
28. ANS:
p is not equal to q.
PTS: 1
DIF: L2
OBJ: 5-4.2 Using Indirect Reasoning
TOP: 5-4 Example 3
REF: 5-4 Inverses, Contrapositives, and Indirect Reasoning
STA: CA GEOM 2.0
KEY: indirect reasoning | indirect proof
3