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

Geometry
Assignment 5G
Finding the Error in Proofs
Name _____________________________
Period ________ Date ________________
For questions 1-4, decide which congruence
postulate, if any, you can use to prove that
the given triangles are congruent.
5.
What additional information is needed
to prove the triangles congruent using
HL?
Write the congruence statement and
identify the postulate.
XYZ  ______by _______
1.
Q
Y
P
____________________________
6.
Z
R
What additional information is needed
to prove the triangles congruent using
SAS?
X
BCF  ______by _______
2.
B
D
____________________________
C
F
E
7.
Given the diagram below.
Z
X
ABC  ______by _______
3.
C
B
D
E
Y
V
W
A
F
LMN  ______by _______
4.
R
M
L
N
Revised 10/23/2011
Q
If VY  XY , which congruence
postulate/theorem justifies
VYZ  XYE ?
a.
SSS
b.
SAS
c.
ASA
d.
AAS
e.
HL
S
page 1 of 4
Printed 10/30/2012
Geometry
Assignment 5G
Finding the Error in Proofs
Name _____________________________
Period ________ Date ________________
ONE OF THE REASONS IN THE
FOLLOWING PROOF IS INCORRECT.
ONE OF THE REASONS IN THE
FOLLOWING PROOF IS INCORRECT.
Given: AB  DE , BC  EF , AC  DF
Given: PN bisects MNO , MN  NO
Prove: MNP  ONP
Prove: ABC  DEC
A
N
D
B
C
F
E
M
Statements
1. AB  DE
2. BC  EF
Reasons
1. Given
2. Given
3. AC  DF
3. Reflexive
Property
4. ABC  DEF
4. SSS
8. Which reason in the above proof is
incorrect?
O
P
Statements
1. PN bisects MNO
MN  NO
Reasons
1. Given
2. MNP  ONP
2. Alternate
Interior Angles
of Parallel
Lines are
Congruent
3. NP  NP
3. Reflexive
Property
4. MNP  ONP
4. SAS
9. What is the correct reason?
10.
Given
a  b .
m1   3x  60  and m2   6x  30  .
o
o
11. Which reason in the above proof is
incorrect?
12. What is the correct reason?
What term best describes
angles 1 and 2?
What are m1 and m2?
1
2
Revised 10/23/2011
a
b
page 2 of 4
Printed 10/30/2012
Geometry
Assignment 5G
Finding the Error in Proofs
Name _____________________________
Period ________ Date ________________
ONE OF THE REASONS IN THE
FOLLOWING PROOF IS INCORRECT.
Complete the following proof.
Given: B and D are right angles;
C is the midpoint of BD ; AC  EC
15. Given: AB  CD , BC  DA
Prove: BAD  DCB
Prove: ABC  EDC
A
B
E
D
C
Statements
Reasons
1. B and D are
right angles
1. Given
B
C
A
D
Statements
1. AB  CD ,
BC  AD
Reasons
1. Given
2.
2. Reflexive
Property
3. BAD  DCB
3.
AC  EC
2. B  D
2. All right angles
are congruent
(Euclid)
3. C is the midpoint
of BD
3.
4. BC  DC
4. Definition of
Midpoint
5. ABC  EDC
5. SAS
Given
16.
13. Which reason in the above proof is
incorrect?
Error Analysis
Your friend claims isosceles triangles
are congruent when any two sets of
corresponding sides are congruent.
He explains that since two sides are
the same, the third side must always
be congruent.
Explain the error in his reasoning.
Provide pictures in your counter
example.
14. What is the correct reason?
Revised 10/23/2011
page 3 of 4
Printed 10/30/2012
Geometry
Assignment 5G
Finding the Error in Proofs
17.
Name _____________________________
Period ________ Date ________________
Something is wrong in the following proof. Find the error. Then
fix the proof so that it is correct.
Given: A  C
BD bisects ADC
Prove:
ADB  CDB
Statements
1.
A  C
1. Given
2.
BD bisects ADC
2. Given
3. ADB  CDB
3. All right angles are congruent
4. BD  BD
4. Reflexive Property
5.
18.
Reasons
ADB  CDB
5. AAS
Something is wrong in the following proof. Find the error. Then
fix the proof so that it is correct.
Given: AB  CD
AD  BC
Prove: A  C
Statements
Reasons
6.
AB  CD
1. Given
7.
AD  BC
2. Given
8.
BD  DB
3. Reflexive Property
9.
ADB  CDB
10. A  C
Revised 10/23/2011
4. SAS
5. CPCTC
page 4 of 4
Printed 10/30/2012