Name: ________________________ Class: ___________________ Date: __________
Chapter 2 Test
____
____
1. Based on the pattern, what are the next two terms of the sequence?
9, 15, 21, 27, . . .
A. 33, 972
B. 39, 45
C. 162, 972
2. Based on the pattern, what are the next two terms of the sequence?
9 9
9
9
9, ,
,
,
,...
5 25 125 625
9
9
9
9
A.
,
C.
,
3125 3130
3125 15625
B.
____
9
9
,
630 3130
D.
9
9
,
630 635
3. Based on the pattern, what is the next figure in the sequence?
A.
____
D. 33, 39
B.
C.
D.
4. What is a counterexample for the conjecture?
Conjecture: The product of two positive numbers is greater than the sum of the two numbers.
A. 3 and 5
B. 2 and 2
C. A counterexample exists, but it is not shown above.
D. There is no counterexample. The conjecture is true.
____
____
5. What is a counterexample for the conjecture?
Conjecture: Any number that is divisible by 4 is also divisible by 8.
A. 24
B. 40
C. 12
6. What is the conclusion of the following conditional?
A number is divisible by 2 if the number is even.
A. The sum of the digits of the number is divisible by 2.
B. If a number is even, then the number is divisible by 2.
C. The number is even.
D. The number is divisible by 2.
1
D. 26
ID: A
Name: ________________________
____
ID: A
7. Write this statement as a conditional in if-then form:
All triangles have three sides.
A. If a triangle has three sides, then all triangles have three sides.
B. If a figure has three sides, then it is not a triangle.
C. If a figure is a triangle, then all triangles have three sides.
D. If a figure is a triangle, then it has three sides.
____
8. Draw a Venn diagram to illustrate this conditional:
Cars are motor vehicles.
A.
C.
B.
____
D.
9. A conditional can have a ____ of true or false.
A. hypothesis
C. counterexample
B. truth value
D. conclusion
2
Name: ________________________
ID: A
____ 10. Which statement is a counterexample for the following conditional?
If you live in Springfield, then you live in Illinois.
A. Sara Lucas lives in Springfield.
B. Jonah Lincoln lives in Springfield, Illinois.
C. Billy Jones lives in Chicago, Illinois.
D. Erin Naismith lives in Springfield, Massachusetts.
____ 11. Use the Law of Detachment to draw a conclusion from the two given statements.
If two angles are complementary, then the sum of their measures is 90°.
E and F are complementary.
A. mE + mF = 180
C. mE  mF
B. E is congruent to F.
D. mE + mF = 90
____ 12. What is the value of x? Identify the missing justifications.
mPQR  x  5, mSQR  x  7, and mPQS  100.
mPQR  mSQR  mPQS
x – 5 + x – 7 = 100
2x – 12 = 100
2x = 112
x = 56
a. __________
b. Substitution Property
c. Simplify
d. __________
e. Division Property of Equality
A. Angle Addition Postulate; Subtraction Property of Equality
B. Angle Addition Postulate; Addition Property of Equality
C. Protractor Postulate; Addition Property of Equality
D. Protractor Postulate; Subtraction Property of Equality
3
Name: ________________________
ID: A
____ 13. BD bisects ABC. mABC = 7x. mABD = 3x  36. Find mDBC.
A. 108
B. 72
C. 180
D. 252
____ 14. Name the Property of Equality that justifies this statement:
If l = m, then m  l .
A. Multiplication Property
C. Subtraction Property
B. Symmetric Property
D. Transitive Property
____ 15. Which statement is an example of the Addition Property of Equality?
A. If p = q then p  s  q  s.
C. If p = q then p  s  q  s.
B. If p = q then p  s  q  s.
D. p = q
Use the given property to complete the statement.
____ 16. Transitive Property of Congruence
If CD  EF and EF  GH , then ______.
A. EF  EF
B. CD  EF
____ 17. Multiplication Property of Equality
If 5x  9  36, then ______.
A. 5x  324
B. 5x  9  324
____ 18. Substitution Property of Equality
If y  5 and 7x  y  11, then ______.
A. 7(5)  y  11
B. 7x  5  11
C. EF  GH
D. CD  GH
C. 36  5x  9
D. 36  5x  9
C. 7x  5  11
D. 5  y  11
____ 19. Name the Property of Congruence that justifies the statement:
If MN  LK , then LK  MN .
A. Symmetric Property
C. Reflexive Property
B. Transitive Property
D. none of these
4
Name: ________________________
ID: A
____ 20. Name the Property of Congruence that justifies this statement:
If A  B and B  C, then A  C .
A. Transitive Property
C. Reflexive Property
B. Symmetric Property
D. none of these
____ 21. Complete the two-column proof.
Given: 12x  6y  5; x  5
Prove:
65
y
6
12x  6y  5; x  5
a. ________
60  6y  5
b. ________
6y  65
c. ________
65
6
d. ________
y
65
y
e. ________
6
A. a. Given
b. Substitution Property
c. Addition Property of Equality
d. Division Property of Equality
e. Symmetric Property of Equality
B. a. Given
b. Substitution Property
c. Addition Property of Equality
d. Addition Property of Equality
e. Symmetric Property of Equality
C. a. Given
b. Symmetric Property of Equality
c. Addition Property of Equality
d. Division Property of Equality
e. Reflexive Property of Equality
D. a. Given
b. Substitution Property
c. Addition Property of Equality
d. Division Property of Equality
e. Reflexive Property of Equality
5
Name: ________________________
ID: A
____ 22. Complete the two-column proof.
Given:
x
 9  11
5
Prove: x  10
x
 9  11
5
x
2
5
a. ________
b. ________
x  10
c. ________
A. a. Given
b. Subtraction Property of Equality
c. Division Property of Equality
B. a. Given
b. Subtraction Property of Equality
c. Multiplication Property of Equality
C. a. Given
b. Addition Property of Equality
c. Multiplication Property of Equality
D. a. Given
b. Addition Property of Equality
c. Division Property of Equality
____ 23. What is the value of x?
A. –16
B. 120
C. 60
D. 16
B. 36
C. 120
D. 60
____ 24. What is the value of x?
A. 84
6
Name: ________________________
ID: A
____ 25. m2  30. Find m4.
A. 150
B. 30
C. 160
____ 26. Find the values of x and y.
A. x = 15, y = 17
C. x = 68, y = 112
B. x = 112, y = 68
D. x = 17, y = 15
7
D. 20
Name: ________________________
ID: A
27. What is the value of x? Identify the missing justifications.
mAOC  150
mAOB  mBOC  mAOC
a. ____
2x  6(x  3)  150
b. ____
2x  6x  18  150
c. ____
8x  18  150
d. ____
8x  168
e. ____
x  21
f. ____
28. Solve for x. Justify each step.
4x  9  99
29. Complete the paragraph proof.
Given: 1 and 2 are supplementary, and 2 and 3 are supplementary.
Prove: 1  3
By the definition of supplementary angles, m1  m2  _____ (a) and m2  m3  _____ (b). Then
m1  m2  m2  m3 by _____ (c). Subtract m2 from each side. You get m1  _____ (d), or
1  _____ (e).
8
Name: ________________________
ID: A
30. Complete the two-column proof.
Given: 1  2, m1  130
Prove: m3  130
Drawing not to scale
1  2, m1  130
a. _____
m2  130
b. _____
m2  m3
c. _____
m3  130
d. _____
31. Given: 1 and 2 are supplementary, and 1  3.
Prove: 3 and 2 are supplementary.
9
ID: A
Chapter 2 Test
Answer Section
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
D
C
B
B
C
D
D
A
B
D
D
B
D
B
B
D
A
B
A
A
A
B
D
D
B
A
a. Angle Addition Postulate
b. Substitution Property
c. Distributive Property
d. Simplify
e. Addition Property of Equality
f. Division Property of Equality
28.
4x  9  99
4x  9  9  99  9
4x  108
4x
108

4
4
x = 27
Given
Addition Property of Equality
Simplify
Division Property of Equality
Simplify
1
ID: A
29. a. 180
b. 180
c. Transitive Property (or Substitution Property)
d. m3
e. 3
30.
[4] a. Given
b. Substitution Property
c. Vertical Angles Theorem
d. Substitution Property
[3] three parts correct
[2] two parts correct
[1] one part correct
31.
[4] 1 and 2 are supplementary, because it is given. So, m1  m2  180 by the definition
of supplementary angles. 1  3 because it is given. So, m1  m2 by the definition of
congruent angles. By the Substitution Property, m3  m2  180, so by the definition of
supplementary angles, 3 and 2 are supplementary.
OR
equivalent explanation
[3] one step missing OR one incorrect justification
[2] two steps missing OR two incorrect justifications
[1] correct steps with no explanations
2