U4 Quiz Review

Shivers - Intensified Geometry
Unit 4 Quiz Review
You MUST show ALL work to receive full credit!
Name
Period: _
Directions 1-6: In each of the diagrams below use the information given to name all pairs of
congruent triangles you can identify (without
drawing more segments or naming more points).
*You
(a) Write down the triangle congruence statements and (b) explain why the triangles are
congruent. If there are not any pairs of triangles in a given diagram that are congruent, state so.
1.
X is the midpoint of BC ; AB  DC
2.
(a)_______________
(a)_______________
(b)_______________
(b)_______________
T
A
S
60 
50 
X
B
C
70 
D
60 
R
P
3. PQ  RS ; QT  ST
AO  plane M ; BAO  CAO
4.
(a)_______________
(a)_______________
(b)_______________
(b)_______________
A
P
R
M
T
B
Q
C
O
S
5. AF  BF ; FC  FD
(a)_______________
(a)_______________
(b)_______________
(b)_______________
W
D
A
F
C
ZW  ZX ; WY  XY
6.
Z
B
Y
X
Directions 7-9: Given that JRX  QSY , complete each statement.
7. RX  ___________
8. J  ____________
9. RJX  _______________
Questions 10-12: Fill in the missing word with sometimes, always, or never to complete the statement.
10. A right triangle is _________________ congruent to another right triangle.
11. If ABC  XYZ , A is ___________________ congruent to Z .
12. If ABC  XYZ , B is ___________________ congruent to Y .
Questions 13-16: Construct the following: (Be sure to leave all markings!)
14. The perpendicular bisector of AB
13. A line perpendicular to line m through point X
X
m
15. The angle bisector of ABC
A
B
16. A line parallel to the given line through point F
F
Q
R
Questions 17-22: Complete the following proofs.
17.
Given: B is the midpoint of AC
18.
DA  DC
Given: PQ and RS bisect each other at X
Prove: PXR  QXS
Prove: ABD  CBD
P
D
S
R
X
Q
A
19.
B
Given:
C
SA bisects DAR and DTR
20.
Prove: DAT  RAT
D
Z
W
1 2
3 4 T
S
Given: X  Y
XO  YO
Prove: WO  ZO
5
6
O
A
X
Y
R
21.
Given: PR bisects QPS and QRS
22.
Prove: RQ  RS
Given: AD ME; MD BE
M is the midpoint of AB
Prove: D  E
Q
D
P
E
R
A
S
M
B
Answer Key:
1.
3.
5.
TSR  TPR; ASA
No congruent triangles
AFC  BFD; SAS
7. SY
9. SQY
11. sometimes
2.
4.
6.
No congruent triangles
ABO  ACO; ASA
ZWY  ZXY ; SSS
8. Q
10. sometimes
12. Always
13 – 16: Constructions: Be sure to have all proper markings.
Refer back to your constructions packet for guidance/refresher!
Note with the proofs, there are multiple solutions to these problems.
17. Since B is the midpoint of AC , by definition AB  BC .
BD  BD by the reflexive prop., and we know DA  DC , so by SSS ABD  CBD
18. Since PQ and RS bisect each other at X, X is the midpoint of PQ and RS
by definition of a segment bisector.
By the definition of a midpoint, PX  XQ and RX  XS
Vertical angles are congruent so PXR  QXS .
We can now say PXR  QXS because of SAS
19. Since AS bisects DAR and DTR , 5  6 and 1  3 by definition.
By the Angle Addition Postulate, m1  m2  180 and m3  m4  180 ,
so by definition 1 and 2 are supplementary as well as 3 and 4 .
Since we have two angles supplementary to congruent angles, 2  4 .
AT  AT by the reflexive property, so DAT  RAT by ASA
20. WOX  ZOY by Vertical angles theorem
Since X  Y and XO  YO , WOX  ZOY by SAS
Therefore WO  ZO by the definition of congruent triangles.
21. Since PR bisects QPS and QRS , QPR  RPS and QRP  PRS by definition.
PR  PR by the reflexive property, so PRQ  PRS by ASA.
Therefore RQ  RS by the definition of congruent triangles.
22. A  EMB by corresponding angles postulate, since AD ME .
B  DMA by corresponding angles postulate, since MD BE .
By the Third Angle Theorem (if two angles in one triangle are congruent to two angles in another
triangle, then the third angles are congruent) D  E

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