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Chapter 8 Assessments 1177
8
1. In the figure shown, ___
QX ___
XP , ___
RP ___
XP , ___
QT > ___
RS , and ___
XS > ___
TP . Determine whether XQT is congruent to PRS. Explain your reasoning.
P
Q
R
ST
X
2. Triangle CLG and n AER are isosceles triangles with ___
CL > ___
AE , ____
HG > ___
ZR , and /L > /E. Prove that ___
CH > ___
AZ . Explain your reasoning.
G
H
C
L
Z
R
A
E
Pre-Test
Name Date
451444_Assess_Ch08_1177-1188.indd 1177 04/04/14 10:43 AM
© C
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1178 Chapter 8 Assessments
8Pre-Test page 2
3. Create a two-column proof.
Given: ___
LN bisects /KLM
___
KN > ____
NM
Prove: mK > m/M
L
KN
M
451444_Assess_Ch08_1177-1188.indd 1178 04/04/14 10:43 AM
© C
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Chapter 8 Assessments 1179
8
1. In the figure shown, ____
AW ____
WY , ___
UY ____
WY , ____
WZ ___
YT , and ___
AT ___
UZ . Determine whether AWT is congruent to UYZ. Explain your reasoning.
Y
A
Z
U
TW
2. Triangle RGV and MLF are isosceles triangles, with vertex angles G and L, ___
RG > ___
ML , G > L, ___
V T bisects GVR, and ___
FN bisects LFM. Prove that ___
V T > ___
FN . Explain your reasoning.
R
T
G
V M
N
L
F
Post-Test
Name Date
451444_Assess_Ch08_1177-1188.indd 1179 04/04/14 10:43 AM
© C
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Lear
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1180 Chapter 8 Assessments
8 3. Create a two-column proof.
Given: ___
BD bisects ABC
___
AD ___
DC
Prove: ___
AB ___
BC
A
B
CD
Post-Test page 2
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Chapter 8 Assessments 1181
8
1. Using the figure shown, determine whether RAC is congruent to YTC. Explain your reasoning.
R
CA
T
Y
2. In the figure shown, ‹
___ › DO
‹
___ › AB , ‹
___ › OB
‹
___ › DE , ‹
___ › AB >
‹
___ › DO , and
___ AO >
___ OE . Prove AOB > OED.
AB
O
E
D
T
Mid-Chapter Test
Name Date
451444_Assess_Ch08_1177-1188.indd 1181 04/04/14 10:43 AM
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1182 Chapter 8 Assessments
8Mid-Chapter Test page 2
3. In the figure shown, NWL HWL and ___
LW ___
NH . Prove NLW HLW.
28° 28°
N WH
L
4. In the figure shown, ZG 1 GC 5 36, ZG 5 18, and ___
GT ___
ZC . Prove ZGT > CGT.
T
G
CZ
451444_Assess_Ch08_1177-1188.indd 1182 04/04/14 10:43 AM
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Chapter 8 Assessments 1183
8End of Chapter Test
Name Date
1. In the figure shown, ACB is an isosceles triangle with CAB > CBA. In addition, ___
DC ___
CE . Prove ADC BEC. Explain your reasoning.
A B
CD E
2. In the figure shown below, J X and ___
JD > ___
XD . Determine whether ___
BD ___
CD . Explain your reasoning.
B C
J X
D
451444_Assess_Ch08_1177-1188.indd 1183 04/04/14 10:43 AM
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1184 Chapter 8 Assessments
8End of Chapter Test page 2
3. Create a two-column proof.
Given: D R
___
DT ___
TR
Prove: GTD GTR
D
G
RT
4. Using the figure shown, determine whether HAW TAW. Explain your reasoning.
H
A
T
W
451444_Assess_Ch08_1177-1188.indd 1184 04/04/14 10:43 AM
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Chapter 8 Assessments 1185
8Standardized Test Practice
Name Date
1. Which is the inverse of the following statement? If an integer is odd, then it is not divisible by 2.
a. If an integer is odd, then it is not divisible by 2.
b. If an integer is not odd, then it is not divisible by 2.
c. If an integer is not odd, then it is divisible by 2.
d. If an integer is not divisible by 2, then it is odd.
2. In the figure shown, ___
PS ___
RQ . Which theorem can be used to prove SQR QSP?
a. SSS
b. SAS
c. AAS
d. HL
P Q
RS
3. In the figure shown, ABD and BCD are isosceles triangles and ABD CBD. Which theorem can be used to prove ABD CBD?
a. SSS
b. SAS
c. AAS
d. HL
B
AD
C
4. Which is the contrapositive of the following statement? If quadrilateral ABCD is a rectangle, then quadrilateral ABCD is a square.
a. If quadrilateral ABCD is a square, then quadrilateral ABCD is a rectangle.
b. If quadrilateral ABCD is not a square, then quadrilateral ABCD is not a rectangle.
c. If quadrilateral ABCD is not a rectangle, then quadrilateral ABCD is not a square.
d. If quadrilateral ABCD is not a square, then quadrilateral ABCD is a rectangle.
5. In the figure, CAN is isosceles, Q is the midpoint of ___
AC , and V is the midpoint of ___
AN . What information is needed to prove CQH NVH?
a. AQH AVH
b. ____
QH ___
VH and ___
CH ___
NH
c. ____
QH ___
VH and QHC VHN
d. HCN HNC and QHC VHN
A
C
VQ
N
H
451444_Assess_Ch08_1177-1188.indd 1185 04/04/14 10:43 AM
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1186 Chapter 8 Assessments
8Standardized Test Practice page 2
6. Points G, E, and P form a triangle. Also, ___
GE ___
TR , ___
GP ___
TQ , and ___
PE ___
QR . Which triangle is GEP congruent to?
a. RTQ
b. QTR
c. TQR
d. TRQ
7. Which of the following cannot be used to show that the right triangles shown are congruent?
a. ____
KM ___
RT and ___
KL ___
RS
b. ___
LM ___
ST and ___
KL ___
RS
c. K R and L S
d. ____
KM ___
RT and K R K
L
M R
S
T
8. Using the diagram shown, choose the correct conclusion.
a. The triangles are congruent by HL.
b. The triangles are congruent by LA.
c. The triangles are congruent by HA. 200
200
d. Not enough information to determine if the triangles are congruent.
9. Given an isosceles triangle, which of the following is not true?
a. Base angles are congruent.
b. Angle bisectors to congruent sides are not congruent.
c. Altitudes to congruent sides are congruent.
d. The altitude from the vertex angle divides the triangle into congruent triangles.
10. Using the diagram shown, choose the correct conclusion.
A
R
T
Y
C
a. The triangles are congruent by HL.
b. The triangles are congruent by HA.
c. The triangles are congruent by LA.
d. All of the above.
451444_Assess_Ch08_1177-1188.indd 1186 04/04/14 10:43 AM
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Chapter 8 Assessments 1187
8Standardized Test Practice page 3
Name Date
Use the figure shown to answer Questions 11 and 12.
U G A N
B
11. Triangle BUN is isosceles with ___
BU ___
BN . What additional given information is needed to prove BUG BNA by ASA?
a. UBA NBG
b. UBG NBA
c. BGU BAN
d. BUG BNA
12. Triangle BAG is isosceles with ___
BG ___
BA . What is one additional piece of information that is needed to prove BGN BAU by SAS?
a. ____
GN AU
b. ___
BU ___
BN
c. ____
GU ___
AN
d. ___
AG ___
GA
13. Which of the following is not true in any isosceles triangle?
a. The altitude to the base does not separate the triangle into congruent triangles.
b. The altitude to the base bisects the base.
c. The altitude to the base is the perpendicular bisector of the base.
d. The altitude to the base bisects the vertex angle.
14. In the figure shown, ____
GM ____
MO and ___
EO ____
MO . Which theorem can be used to prove GMO EOM?
a. LL
b. LA
c. HL
d. HA
M
G E
O
T
451444_Assess_Ch08_1177-1188.indd 1187 04/04/14 10:43 AM
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1188 Chapter 8 Assessments
8Standardized Test Practice page 4
15. Which of these cannot be used to prove that two triangles are congruent?
a. AA
b. SAS
c. AAS
d. HL
16. If ABC XYZ, which of the following is not true?
a. A X
b. ___
AC ___
XZ
c. ___
BC ___
YZ
d. ___
AB ___
YZ
17. Given the statement, If a number is a multiple of 6, then it is a multiple of 3, which of the following is true?
a. If a number is not a multiple of 3, then it is not a multiple of 6.
b. If a number is not a multiple of 6, then it is not a multiple of 3.
c. If a number is not a multiple of 6, then it is a multiple of 3.
d. If a number is a multiple of 6, then it is not a multiple of 3.
18. In the figure shown, ___
OA ___
OB . Which additional piece of information can be used to show that the triangles are congruent?
a. ___
XO ___
TO
b. ___
XA ___
TB
c. ___
AO ___
BO
d. ___
XB ___
TA A B
X
O
T
19. Which of the following are needed to show that ABC and XYZ, with right angles at C and Z, are congruent by the HL Congruence Theorem?
I. ___
AB ___
XY II. B Y III. A X IV. ___
AC ___
XZ
a. III
b. IV
c. II
d. I and IV
20. In the figure shown, ___
DT ___
RS . Which of the following is not true?
a. S T
b. ___
GS ___
GT
c. GST is not isosceles.
d. DGT RGS D
G
RTS
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