Download For questions 1-9, decide which congruence postulate, if any, you

Geometry
Assignment 5E
Name _____________________________
Period ________ Date ________________
For questions 1-9, 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.
1.
B
6.
F
Q
Y
C
D
P
G
E
Z
R
2.
X
G
H
E
F
7.
B
3.
A
D
C
D
F
E
C
B
E
8.
C
4.
R
3"
T
C
2"
2"
S
3"
B
D
E
A
A
F
B
9.
5.
R
M
L
N
Created 6/2010
Q
S
Printed 4/28/2017
Geometry
Assignment 5E
10.
Name _____________________________
Period ________ Date ________________
Given the diagram below.
12.
Given the diagram below.
F
Z
I
X
Y
V
J
W
H
G
If VY  XY , which congruence
postulate/theorem justifies
VYZ  XYE ?
Which corresponding parts need to
be congruent in order to prove
FJH  GJI by SSS?
a.
b.
c.
d.
11.
HJF  IJG
FJ  GJ
FH  GI
FHJ  GIJ
Given the diagram below.
A
E
F
a.
SSS
b.
SAS
c.
ASA
d.
AAS
e.
HL
For #13-15, the proof is in the incorrect
order. Write a correct order of the steps for
each proof.
13. Given: FH bisects GFJ and GHJ
C
B
D
Prove:  GFH   JFH
G
If BC  EF , which congruence
postulate/theorem justifies that
ABC  DEF ?
a.
b.
c.
d.
e.
HL
SAS
SSS
AAS
ASA
Created 6/2010
F
2
1
3
4
H
J
Statement
1. 2  1
3  4
Reason
1. Definition of
angle bisector
2.  GFH   JFH
2. ASA
3. FH bisects
GFJ and GHJ
3. Given
4. FH  FH
4. Reflexive property
Printed 4/28/2017
Geometry
Assignment 5E
14.
Name _____________________________
Period ________ Date ________________
Given: AB  AD and DE  AD
BC  EC
For # 16-18, one of the reasons is incorrect.
Which reason is wrong? Write the correct
reason.
Prove: ABC  DEC
16. Given: AB  DE , BC  EF ,
E
AC  DF
Prove: ABC  DEC
A
C
A
D
D
B
B
Statement
1. ACB  DCE
Reason
1. Vertical Angles
Theorem
2. A  D
2. all right angles
are congruent
(Euclid)
3. AB  AD
DE  AD
BC  EC
4.
ABC  DEC
5. A and D
are right angles
15.
C
F
E
Statement
1. AB  DE
2. BC  EF
Reason
1. Given
2. Given
3. AC  DF
3. Reflexive
Property
4. ABC  DEF
4. SSS
3. Given
4. AAS
17.
5. Definition of
perpendicular
Given: MH  MK ; HJ  KJ
MJH and MJK are right angles
Given: PN bisects MNO ,
MN  NO
Prove: MNP  ONP
N
M
M
Prove: H  K
H
J
K
O
P
Statement
1. PN bisects MNO ;
MN  NO
Reason
1. Given
Statement
1. MJH  MJK
Reason
1. HL
2. MJH  MJK
2. All right angles
are congruent
(Euclid)
2. MNP  ONP
2. AIA
Congruence
Theorem
3. H  K
3. CPCTC
3. NP  NP
4. MH  MK ; HJ  KJ
MJH and MJK
are right angles
3. Reflexive
Property
4. Given
4. MNP  ONP
4. SAS
Created 6/2010
Printed 4/28/2017
Geometry
Assignment 5E
18.
Name _____________________________
Period ________ Date ________________
Given: B and D are right angles;
C is the midpoint of BD ;
AC  EC
20. Given: AB  CD , BC  DA
Prove: BAD  DCB
Prove: ABC  EDC
A
B
D
C
2. B  D
2. All right angles
are congruent
(Euclid)
3. BC  DC
3. Definition of
Midpoint
4. ABC  EDC
4. SAS
A
D
Statement
1. AB  CD ,
BC  AD
Reason
1. Given
2.
2. Reflexive
Property
3. BAD  DCB
3.
21.
M
19. Given: HJ  KJ ,
MJH  MJK
Prove: MJH  MJK
H
Statement
1. HJ  KJ , MJK  MJK
Given the diagram below and
a  b . If the m1  3x  60 and
m2  6x  30 , then what is the
m1 and m2?
For #19-20 fill in the missing part of the
proof.
J
K
Reason
1. Given
22.
3. MJH  MJK
C
E
Statement
Reason
1. B and D are
1. Given
right angles;
C is the midpt of BD ;
AC  EC
2. MJ  MJ
B
2.
In the diagram below, a b.
Find m 1 and m2, if
m1 = 5a and m2 = 2a + 12.
t
a
1
3.
b
2
Created 6/2010
Printed 4/28/2017
Geometry
Assignment 5E
Name _____________________________
Period ________ Date ________________
For #23-24, is the argument valid or invalid?
If it’s invalid, provide a counterexample.
28.
Find the slope of the line parallel to
the graph of y 
23.



If today is Friday, I’m eating fish for
dinner.
Today is Friday the 13th.
Therefore, tonight I’m eating fish for
dinner.
4
3
x–
2
3
.
29.
What is the slope of the line
perpendicular to the graph of
3x + 2y = 8?
30.
Write the equation of a line that has
a y-intercept of –3 and is parallel to
2
the graph of y  x .
3
24.



A square has four congruent sides.
Polygon ABCD has four congruent
sides.
Therefore, polygon ABCD is a
square.
For #25-27, using the drawing below.
R
Q
N
P
O
25.
Name one line that is parallel to PO .
26.
Name two lines that are
perpendicular to PO .
27.
Name two lines that are skew to PO .
Created 6/2010
Printed 4/28/2017