Download Geometry Unit 5 Corrective 1

Geometry Unit 5 Corrective 1
Name: ____________________________
1._____ 2._____ 3._____ 4. _____ 5. _____
Period: _______ Date: ______________
Competency 1: Identify Congruence
For questions 1 – 5, decide which
congruence postulate, if any, you can use to
prove that the given triangles are congruent.
Write the congruence statement and
identify the postulate.
F
B
4.
C E
D
B
1.
G
E
C
∆BCD ≅ ____________
D
F
A
by _________________
∆ABC ≅ ____________
G
5.
by _________________
H
2.
G
H
K
I
E
F
∆HGF ≅ ____________
J
by _________________
L
∆JKL ≅ ____________
Competency 2: Congruence of Triangles
by _________________
6.
Given the diagram below.
F
I
3.
O
Q
J
H
G
Which corresponding parts need to be
congruent in order to prove
FJH ≅ GJI by SSS?
P
N
M
∆NOP ≅ ____________
a. ∠HJF ≅ ∠IJG
by _________________
b. FJ ≅ GJ
c. FH ≅ GI
d. ∠FHJ ≅ ∠GIJ
Revised 10/18/2010
page 1 of 6
Printed 10/18/2010
Geometry Unit 5 Corrective 1
Name: ____________________________
1._____ 2._____ 3._____ 4. _____ 5. _____
Period: _______ Date: ______________
Competency 3: Completing Proofs
7.
Given the diagram below.
For the two partial proofs below, supply the
missing statements or reasons.
K
L
10.
Prove: ∆ ABD ≅ ∆ CBD
D
J
I
Given: AD ≅ CD ; B is midpoint of AC
Which corresponding parts need to be
congruent in order to prove
KIL ≅ IKJ by ASA?
A
a. LK ≅ JI
Statement
1. AD ≅ CD
B is midpoint of AC
Reason
1. Given
2. AB ≅ CB
2.
3. BD ≅ BD
3. Reflexive
E
4. ∆ABD ≅ ∆CBD
4.
D
11.
b. KI ≅ IK
∠KLJ ≅ ∠IJK
c.
C
B
d. ∠LIK ≅ ∠JKI
8.
Given the diagram below.
A
F
C
B
If BC ≅ EF , which congruence
postulate/theorem justifies that
ABC ≅ DEF ?
a. HL
b. SAS
9.
S
c. SSS
d. AAS
e. ASA
U
T
S
X
If ∠SRT ≅ ∠UXT , which congruence
postulate/theorem justifies that
STR ≅ UTX ?
a. ASA
c. SSS
Revised 10/18/2010
b. SAS
d. AAS
W
T
Given the diagram below.
R
Given: ∠ X ≅ ∠ W, XT ≅ WT
Prove: ST ≅ VT
X
V
Statement
1. ∠ X ≅ ∠ W
XT ≅ WT
Reason
1. Given
2. ∠ STX ≅ ∠ VTW
2. Vertical Angles
Theorem
3. ∆STX ≅ ∆VTW
3.
4.
4. CPCTC
e. HL
page 2 of 6
Printed 10/18/2010
Geometry Unit 5 Corrective 1
Name: ____________________________
1._____ 2._____ 3._____ 4. _____ 5. _____
Period: _______ Date: ______________
12.
Given:
DR ⊥ AG ; RA ≅ RG
13.
The following proof is out of order.
Prove:
∆DRA ≅ ∆DRG
Given: O is the midpoint of MQ
O is the midpoint of NP
D
Prove:
∆MON ≅ ∆QOP
M
A
P
G
R
Statements
1. DR ⊥ AG ; RA ≅ RG
Reasons
1. Given
2. ∠DRA and ∠DRG
are right angles
2. Definition of
perpendicular
3. ∠DRA ≅ ∠DRG
3. Vertical Angles
Theorem
Statements
1. O is midpoint of NP
Reasons
1. Given
4. DR ≅ DR
4. Reflexive
Property
2.
2. SAS
5.
∆DRA ≅ ∆DRG
O
N
Q
∆MON ≅ ∆QOP
3. MO ≅ QO
3. Definition of
midpoint
4. ∠MON ≅ ∠QOP
4. Vertical Angles
Theorem
5. SAS
Which reason in the above proof is
incorrect?
5. O is midpoint of MQ 5. Given
What is the correct reason?
6.
NO ≅ PO
6. Definition of
Midpoint
Which of the following choices puts the
statements and reasons in a correct order?
Revised 10/18/2010
a.
4, 3, 5, 1, 6, 2
b.
5, 1, 3, 6, 4, 2
c.
4, 6, 1, 3, 5, 2
d.
5, 6, 3, 4, 1, 2
page 3 of 6
Printed 10/18/2010
Geometry Unit 5 Corrective 1
Name: ____________________________
1._____ 2._____ 3._____ 4. _____ 5. _____
Period: _______ Date: ______________
14.
Competency 4: Geometry Distributed Practice
The following proof is out of order.
15.
Given: ∠G ≅ ∠B ; CB GA
Given the diagram below and a  b:
a
Prove: GC ≅ BA
1
C
2
b
B
o
o
If the m∠1 = ( 8x − 5 ) and m∠2 = ( 2x + 5 ) ,
then what is the m∠1 and m∠2 ?
G
A
Statements
1. CA ≅ AC
Reasons
1. Reflexive
Property
2.
∠G ≅ ∠B
2. Given
3.
∆GCA ≅ ∆BAC
3. AAS
4.
CB GA
4. Given
16A. What is the slope of the line parallel
4
2
x+y=− ?
to the graph of
3
3
16B. What is the slope of the line perpendicular
4
2
x+y=− ?
to the graph of
3
3
5. GC ≅ BA
5. CPCTC
6.
6. Alternate
interior angles
of parallel
lines are
congruent
∠GAC ≅ ∠BCA
17.
Given the diagram below:
D
W
Which of the following choices puts the
statements and reasons in a correct order?
a.
3, 1, 6, 2, 5, 4
b.
4, 6, 2, 5, 1, 3
c.
5, 2, 3, 6, 4, 1
d.
2, 4, 6, 1, 3, 5
Revised 10/18/2010
A
Z
C
B
X
Y
WhatW
two lines are parallel to WZ ?
page 4 of 6
Printed 10/18/2010
Geometry Unit 5 Corrective 1
Name: ____________________________
1._____ 2._____ 3._____ 4. _____ 5. _____
Period: _______ Date: ______________
18.
19.
What is the equation of a line that has
7
a y-intercept of − and is
8
perpendicular to the graph of
5
y=− x?
6
22.
Given the following proportion:
15 x
=
9 6
What is the value of the variable?
Is the following argument valid or
invalid? If it’s invalid, provide a counter
example.
•
If a person is 18 years old, he or
she may vote in a federal election.
•
Kristy is 18 years old.
•
Therefore, Kristy may vote in the
federal election.
23.
Given the following proportion:
4 b+4
=
3
b
What is the value of the variable?
Competency 5: Algebra Distributed Practice
20.
Given the following equation:
24.
-1x – 2 = 5x – 14
What is the value of the variable?
Find the distance between (-2, -5) and
(-1, -6). Give both an exact answer
and an estimated answer to the
nearest tenth.
Distance formula
d=
21.
Given the following equation:
6(b + 3) = 8(b – 4)
What is the value of the variable?
Revised 10/18/2010
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Printed 10/18/2010
Geometry Unit 5 Corrective 1
Name: ____________________________
1._____ 2._____ 3._____ 4. _____ 5. _____
Period: _______ Date: ______________
ANSWERS:
1.
∆ABC ≅ ∆EFD by SAS
2.
∆JKL ≅ ∆GIH by SSS
3.
Not Possible
4.
∆BCD ≅ ∆FEG by HL
5.
∆HGF ≅ ∆EGF by AAS
20.
x=2
21.
b = 25
22.
x = 10
23.
b = 12
24.
6.
C
7.
B
8.
B
9.
D
10.
2. Definition of Midpoint
4. SSS
11.
3. ASA
4. ST ≅ VT
12.
#3, all right angles are congruent
13.
B
14.
D
15.
∠1 = 139°
2 ≈ 1.4
∠2 = 41°
16A. m|| = −
16B. m⊥ =
4
3
3
4
17.
AD & BC & XY (choose 2)
18.
y=
19.
Valid.
6
7
x−
5
8
Revised 10/18/2010
page 6 of 6
Printed 10/18/2010