Download Geo Review C

Diagnostic Test
Page 1
Accelerated Math®: Wednesday, January 11, 2006, 9:49:53 AM
Dr. Kevin Kiyoi
Geometry 10, Per 4
Amador Valley
Practice Geo
Form Number 96140
Objectives: (5 of 5 listed)
31. Proofs: Algebra & properties of equality
32. Proofs: Angle & segment addition
33. Proofs: Angles
34. Proofs: Triangles
35. Proofs: Parallel lines
66. Identify the correct conclusion based on the given information:
Given: ∠1 and ∠2 are complementary angles.
∠1 and ∠3 are complementary angles.
[A] ∠2 ≅ ∠3
[B] ∠1 ≅ ∠3
[C] ∠1 ≅ ∠2
[D] ∠2 and ∠3 are complementary angles.
67. Which reason and statement are missing from the following proof?
Given: n ⊥ m and n ⊥ l
AB ≅ DE
Prove: ∆ABC ≅ ∆EDC
l
m
A
n
B
C
D
E
Statements
Reasons
n ⊥ m and n ⊥ l
Given
AB ≅ DE
Given
∠ABC and ∠EDC are right angles. ?
∆ABC and ∆EDC are right triangles. Definition of right triangle.
?
Vertical angles are congruent.
∆ABC ≅ ∆EDC
LA right triangle congruence theorem
[A] All right angles are congruent.; ∠BAC ≅ ∠DEC
[B] Perpendicular lines form right angles.; ∠ACB ≅ ∠ECD
[C] Vertical angles are congruent.; ∠ACD ≅ ∠ECB
[D] Definition of right angle.; ∠ACB ≅ ∠ECD
Diagnostic Test
Page 2
Accelerated Math®: Wednesday, January 11, 2006, 9:49:53 AM
Geometry 10, Per 4
Form Number 96140
Practice Geo
68. What is the missing reason in the proof below?
Given: m∠M = 62, m∠O = 54
Prove: m∠N = 64
N
M
O
1. m∠M = 62, m∠O = 54
1. Given
2. m∠ M + m∠ N + m∠O = 180 2. ?
3. 62 + m∠N + 54 = 180
3. Substitution property
4. m∠N = 64
4. Subtraction property of equality
[A] Angle Addition Postulate
[B] If two angle are supplementary to the same angle, they are congruent to each other.
[C] The sum of the ∠s in a ∆ is 180° .
[D] Addition property of equality
69. Given: ∠ 3 ≅ ∠ 5
Prove: a || b
4 1
3 2
8 5
7 6
a
b
What reason would be given for step 2 in the proof below?
1. ∠3 ≅ ∠5 1. Given
2. a|| b
2. ?
[A] If two lines are cut by a transversal so that corresponding ∠s are ≅ , then the lines are ||.
[B] If two lines are cut by a transversal so that interior ∠s are ≅ , then the lines are ||.
[C] If two lines are cut by a transversal so that alternate interior ∠s are ≅ , then the lines are ||.
[D] If two lines are cut by a transversal so that supplementary ∠s are ≅ , then the lines are ||.
70. Which statement is an example of the multiplication property?
[A] If x − 4 = –6, then x − 4 + 4 = −6 + 4.
[C] If 2 x = 7, then
1
1
(2 x ) = (7).
2
2
[B] If x = –3, then x + 5 = −3 + 5.
[D] If x = –5, then – 5 = x.
Diagnostic Test
Accelerated Math®: Wednesday, January 11, 2006, 9:49:53 AM
Geometry 10, Per 4
Page 3
Practice Geo
Form Number 96140
71. Supply the missing reason and statement in the two-column proof: Consider
m∠ AFD = m∠5 and m∠ EFB = m∠6
Given: m∠5 = m∠6
C
B
A
Prove: m∠1 = m∠4
D
1 2 3
4
E
F
Statements
Reasons
m∠5 = m∠6
Given
m∠1 + m∠BFD = m∠5, m∠4 + m∠BFD = m∠6 Angle addition property
m∠1 = m∠5 − m∠BFD, m∠4 = m∠6 − m∠BFD ?
?
Subtraction property of equality
m∠1 = m∠4
Substitution
[A] Subtraction property of equality; m∠5 − m∠BFD = m∠6 − m∠BFD
[B] Addition property of equality; m∠5 + m∠BFD = m∠6 + m∠BFD
[C] Transitive property; m∠5 − m∠BFD = m∠6 − m∠BFD
[D] Transitive property; m∠5 + m∠BFD = m∠6 + m∠BFD
72. Given: ∠ 2 is supplementary to ∠ 5
Prove: a || b
4 1
3 2
8 5
7 6
a
b
What reason would be given for step 2 in the proof below?
1. ∠2 is supplementary to ∠5 1. Given
2. a|| b
2. ?
[A] If two lines are cut by a transversa
transversal are supp., then the line
Diagnostic Test
Page 4
Accelerated Math®: Wednesday, January 11, 2006, 9:49:53 AM
Geometry 10, Per 4
Practice Geo
Form Number 96140
73. Which two-column proof is correct?
Given: ∠ 2 and ∠ 5 are supplementary
Prove: l || m
1
2
3
5
6
7
[A]
[B]
[C]
l
4
8
m
∠2 and ∠5 are suppl.
Given
∠2 ≅ ∠3
Vertical Angles
∠7 and ∠4 are suppl.
Substitution
l || m
Same - side Interior Angles Converse
∠2 and ∠5 are suppl.
Given
∠2 ≅ ∠3
Alternate Exterior Angles
∠3 and ∠5 are suppl.
Alternate Exterior Angles
l || m
Same - side Interior Angles Converse
∠2 and ∠5 are suppl.
Given
∠2 ≅ ∠3
Vertical Angles
∠3 and ∠5 are suppl.
Substitution
l || m
Same - side Interior Angles Converse
[D] none of these
74. In the following proof, which is the reason for the last step?
∠1 and ∠2 are a linear pair
Given
∠1 and ∠2 are supplementary ?
[A] Vertical angles are congruent.
[B] Angles supplementary to the same angle or to congruent angles are congruent.
[C] Linear pair postulate
[D] Angles complementary to the same angle or to congruent angles are congruent.
Diagnostic Test
Page 5
Accelerated Math®: Wednesday, January 11, 2006, 9:49:53 AM
Geometry 10, Per 4
Practice Geo
Form Number 96140
75. Identify the property which justifies the following conclusion: Given: 5e + 30 f
Conclusion: 5 e + 6 f
b
[A] division property
[B] transitive property
[C] distributive property
[D] substitution property
g
76. Supply the missing reason and statement in the two-column proof: Given: AC = BD
Prove: AB = CD
A
B
C
D
E
Statements
Reasons
1. AC = BD
1. Given
2. AC − BC = BD − BC
2. Addition property of equality
3. AB + BC = AC , BC + CD = BD 3. ?
4. ?
4. Addition property
5. AB = CD
5. Substitution
[A] Substitution; AB = AC − BC , CD = BD − BC
[B] Segment addition property; CD = DE , AB = DE
[C] Segment addition property; AB = AC − BC, CD = BD − BC
[D] Substitution; CD = DE , AB = DE
77. Identify the property which justifies the following conclusion: Given: t = u and u = v
Conclusion: t = v
[A] addition property
[B] symmetric property
[C] distributive property
[D] transitive property
Diagnostic Test
Page 6
Accelerated Math®: Wednesday, January 11, 2006, 9:49:53 AM
Geometry 10, Per 4
Form Number 96140
Practice Geo
78. Complete the missing step of the following proof:
Given: x + 9 = − 15; − 15 = y − 10; z + 10 = y
Prove: x = z − 9
Statements
Reasons
x + 9 = − 15; − 15 = y − 10; z + 10 = y
Given
x + 9 = y − 10
Transitive property of equality
z = y − 10
Addition property of equality
x+9 = z
Transitive property of equality
?
?
[A] x = z − 9; Distributive property
[B] x = z − 9; Transitive property of equality
[C] x = z − 9; Reflexive property of equality
[D] x = z − 9; Addition property of equality
79. Identify the correct conclusion based on the given information:
Given: Point B is between points A and C.
Point D is between points B and C.
[A] Point D is between points A and B.
[B] Point D is between points A and C.
[C] Point B is the midpoint of AC.
[D] Point D is the midpoint of BC.
Diagnostic Test
Page 7
Accelerated Math®: Wednesday, January 11, 2006, 9:49:53 AM
Geometry 10, Per 4
Practice Geo
Form Number 96140
80. Which reason and statement are missing from the following proof?
YY
Given: BC AD
Prove:
B
BC ≅ AD
E is the midpoint of BD
E
A
Statements
YY
Reasons
BC AD
Given
BC ≅ AD
Given
C
D
ABCD is a parallelogram ?
?
The diagonals of a parallelogram bisect each other.
E is the midpoint of BD
Definition of bisect
[A] Opposite sides are parallel.; AE = EC
[B] Opposite sides are congruent.; BE = ED
[C] A pair of opposite sides are parallel and congruent.; BE = ED
[D] Alternate interior angles are congruent.; AE = EC
81. Complete the missing step of the following proof:
Given: x − 12 = − 5; − 5 = y + 11; z − 11 = y
Prove: x = z + 12
Statements
Reasons
x − 12 = − 5; − 5 = y + 11; z − 11 = y
Given
x − 12 = y + 11
Transitive property of equality
z = y + 11
Addition property of equality
?
x = z + 12
?
Addition property of equality
[A] x − 12 = z − 11; Transitive property of equality
[B] x − 12 = z − 11; Addition property of equality
[C] x − 12 = z; Addition property of equality
[D] x − 12 = z; Transitive property of equality
Diagnostic Test
Accelerated Math®: Wednesday, January 11, 2006, 9:49:53 AM
Geometry 10, Per 4
82. Supply the missing reason and statement in the two-column proof: Consider
m∠ AFC = m∠5 and m∠ EFC = m∠6
Given: m∠5 = m∠6, m∠2 = m∠3
C
B
A
Prove: m∠1 = m∠4
D
1 2 3
4
E
F
Statements
Reasons
m∠5 = m∠6, m∠2 = m∠3
Given
m∠1 + m∠2 = m∠5, m∠3 + m∠4 = m∠6 Angle addition property
m∠1 + m∠2 = m∠3 + m∠4
?
?
Substitution property
m∠1 = m∠4
Addition property of equality
[A] Reflexive property; m∠1 + m∠2 = m∠2 + m∠4
[B] Reflexive property; m∠1 − m∠2 = m∠2 − m∠4
[C] Substitution property; m∠1 − m∠2 = m∠2 − m∠4
[D] Substitution property; m∠1 + m∠2 = m∠2 + m∠4
83. Which statement is the missing reason from the proof?
∠1 and ∠2 are vertical angles Given
∠1 ≅ ∠2
?
[A] Angles supplementary to the same angle or to congruent angles are congruent.
[B] Supplement Theorem
[C] Angles complementary to the same angle or to congruent angles are congruent.
[D] Vertical angles are congruent.
Page 8
Practice Geo
Form Number 96140
Diagnostic Test
Accelerated Math®: Wednesday, January 11, 2006, 9:49:53 AM
Geometry 10, Per 4
Page 9
Practice Geo
Form Number 96140
84. What is the missing reason in the proof below?
Given: m∠J = 58, m∠K = 60
Prove: m∠L = 62
K
J
1. m∠J = 58, m∠K = 60
L
1. Given
2. m∠ J + m∠ K + m∠ L = 180 2. The sum of the ∠s in a ∆ is 180° .
3. 58 + 60 + m∠L = 180
3. ?
4. m∠L = 62
4. Subtraction property of equality
[A] Addition property of equality
[B] Substitution property
[C] Angle Addition Postulate
[D] If two angle are supplementary to the same angle, they are congruent to each other.
85. Which statement is the missing reason from the proof?
∠1 and ∠2 are a linear pair
Given
∠1 and ∠2 are supplementary Linear pair postulate
m∠1 + m∠2 = 180
?
[A] Definition of supplementary
[B] Vertical angles are congruent.
[C] Angles supplementary to the same angle or to congruent angles are congruent.
[D] Angles complementary to the same angle or to congruent angles are congruent.
Diagnostic Test
Accelerated Math®: Wednesday, January 11, 2006, 9:49:53 AM
Geometry 10, Per 4
Form Number 96140
Page 10
Practice Geo
86. Which two-column proof is correct?
Given: ∠ 8 and ∠ 3 are supplementary
Prove: l || m
1
2
3
5
6
7
[A]
[B]
[C]
l
4
8
m
∠8 and ∠3 are suppl.
Given
∠8 ≅ ∠5
Vertical Angles
∠5 and ∠3 are suppl.
Substitution
l || m
Same - side Interior Angles Converse
∠8 and ∠3 are suppl.
Given
∠8 ≅ ∠5
Alternate Exterior Angles
∠5 and ∠3 are suppl.
Alternate Exterior Angles
l || m
Same - side Interior Angles Converse
∠8 and ∠3 are suppl.
Given
∠8 ≅ ∠5
Vertical Angles
∠7 and ∠1 are suppl.
Substitution
l || m
Same - side Interior Angles Converse
[D] none of these
Diagnostic Test
Page 11
Accelerated Math®: Wednesday, January 11, 2006, 9:49:53 AM
Geometry 10, Per 4
Form Number 96140
Practice Geo
87. Supply the missing reason and statement in the two-column proof: Given: AC = CE , AB = DE
Prove: BC = CD
A
B
C
D
E
Statements
Reasons
1. AC = CE , AB = DE
1. Given
2. AC − AB = CE − AB
2. Addition property of equality
3. AC − AB = CE − DE
3. ?
4. ?
4. Segment addition property
5. BC = AC − AB, CD = CE − DE 5. Addition property of equality
6. BC = CD
6. Substitution
[A] Associative property; AB + BC = AC , CD + DE = CE
[B] Substitution; AB + BC = AC, CD + DE = CE
[C] Associative property; AB + BC = CE , CD + DE = AC
[D] Substitution; AB + BC = CE , CD + DE = AC
Diagnostic Test
Accelerated Math®: Wednesday, January 11, 2006, 9:49:53 AM
Geometry 10, Per 4
88. Which proof is correct?
Given: l m
Prove: ∠ 1 and ∠ 6 are supplementary
YY
YY
[A]
l m
∠1 ≅ ∠4
∠4 and ∠6 are suppl.
∠1and ∠6 are suppl.
YY
[B]
l m
∠1 ≅ ∠4
∠3 and ∠6 are suppl.
∠1and ∠6 are suppl.
YY
[C]
l m
∠1 ≅ ∠4
∠4 and ∠6 are suppl.
∠1and ∠6 are suppl.
Given
Vertical angles
Same-side interior angles
Substitution
Given
Vertical angles
Same-side interior angles
Substitution
Given
Same-side interior angles
Vertical angles
Substitution
Page 12
Practice Geo
Form Number 96140
[D] none of these
Diagnostic Test
Accelerated Math®: Wednesday, January 11, 2006, 9:49:53 AM
Geometry 10, Per 4
Form Number 96140
89. Place the lettered steps from the two-column proof in the correct numbered steps:
C
D
Given: DC ≅ DB, AB ≅ AE
YY
Prove: DC AE
B
A
E
Statements
Reasons
1. DC ≅ DB , AB ≅ AE
2.
3.
4.
5. DC AE
1. Given
(a) ∠C ≅ ∠E
(b) ∠DBC ≅ ∠ABE
(c) ∠C ≅ ∠DBC , ∠E ≅ ∠ABE
Substitution property
Vertical angle theorem
Isosceles triangle theorem
YY
2.
3.
4.
5. Converse of alt. interior angles theorem
[A] 2. (c) 3. (a) 4. (b)
[B] 2. (a) 3. (b) 4. (c)
[C] 2. (a) 3. (c) 4. (b)
[D] 2. (c) 3. (b) 4. (a)
Page 13
Practice Geo
Diagnostic Test
Page 14
Accelerated Math®: Wednesday, January 11, 2006, 9:49:53 AM
Geometry 10, Per 4
Practice Geo
Form Number 96140
90. Supply the missing reason and statement in the two-column proof: Consider
m∠ AFC = m∠5 and m∠ DFB = m∠6
Given: m∠1 = m∠3
C
B
A
Prove: m∠5 = m∠6
D
1 2 3
4
E
F
Statements
Reasons
m∠1 = m∠3
Given
m∠1 + m∠2 = m∠3 + m∠2
Addition property of equality
m∠1 + m∠2 = m∠5, m∠3 + m∠2 = m∠6 ?
?
Substitution
[A] Angle addition property; m∠1 + m∠2 = m∠3 + m∠4
[C] Angle addition property; m∠5 = m∠6
[B] Substitution; m∠5 = m∠6
[D] Substitution; m∠1 + m∠2 = m∠3 + m∠4
End of Assignment