#1
Given: ABC
CD bisects AB
CD  AB
Prove: ACD  BCD
Statement
ABC
CD bisects AB
CD  AB
2. AD  DB Side
Reasons
1.
1. Given
3.
4.
5.
6.
2. A bisector cuts a segment into 2
 parts.
3.  lines form right .
4. All rt  are .
5. Reflexive post.
6. SAS  SAS
CDA and CDB are right 
CDA  CDB Angle
CD  CD Side
ACD  BCD
#2
Given: ABC and DBE bisect each
other.
Prove: ABD  CBD
1.
2.
3.
4.
5.
Statement
ABC and DBE bisect each other.
AB  BC Side
BD  BE Side
ABD and BEC are vertical 
ABD  BEC Angle
ABD  CBD
Reasons
1. Given
2. A bisector cuts a segment into 2
 parts.
3. Intersecting lines form vertical .
4. Vertical  are .
5. SAS  SAS
#1
#3
Given: AB  CD and BC  DA
DAB, ABC, BCD and CDA
are rt 
Prove: ABC  ADC
1.
2.
3.
4.
Statement
AB  CD Side
BC  DA Side
DAB, ABC, BCD and CDA
are rt 
ABC  ADC Angle
ABC  ADC
Reasons
1. Given
2. Given
3. All rt  are .
4. SAS  SAS
#4
Given: PQR  RQS
PQ  QS
Prove: PQR  RQS
Statement
1. PQR  RQS Angle
PQ  QS
Side
2. RQ  RQ
Side
3. PQR  RQS
Reasons
1. Given
2. Reflexive Post.
3. SAS  SAS
#1
#5
Given: AEB & CED intersect at E
E is the midpoint AEB
AC  AE & BD  BE
Prove: AEC  BED
Statement
1. AEB & CED intersect at E
E is the midpoint AEB
AC  AE & BD  BE
2. AEC and BED are vertical
3. AEC  BED Angle
4. AE  EB
Side
5. A & B are rt. 
6. A  B Angle
7. AEC  BED
Reasons
1. Given
2. Intersecting lines form vertical .
3. Vertical  are .
4. A midpoint cut a segment into 2
 parts
5.  lines form right .
6. All rt  are .
7. ASA  ASA
#6
Given: AEB bisects CED
AC  CED & BD  CED
Prove: EAC  EBD
Statement
1. AEB bisects CED
AC  CED & BD  CED
2. CE  ED Side
3. ACE & EDB are rt 
4. ACE  EDB
Angle
Reasons
1. Given
2. A bisector cuts an angle into
2 parts.
3.  Lines form rt .
4. All rt  are 
#1
5. AEC & DEB are vertical 
6. AEC  DEB
Angle
7. EAC  EBD
#7
5. Intersect lines form vertical 
6. Vertical  are 
7. ASA  ASA
Given: ABC is equilateral
D midpoint of AB
Prove: ACD  BCD
Statement
1. ABC is equilateral
D midpoint of AB
2. AC  BC Side
3. AD  DB Side
4. CD  CD
Side
5. ACD  BCD
Reasons
1. Given
2. All sides of an equilateral  are 
3. A midpoint cuts a segment into
2 parts.
4. Reflexive Post
5. SSS  SSS
#8
Given: mA = 50, mB = 45,
AB = 10cm, mD = 50
mE = 45 and DE = 10cm
Prove: ABC  DEF
Statement
1. mA = 50, mB = 45,
AB = 10cm, mD = 50
mE = 45 and DE = 10cm
2. A = D Angle and
B = E Angle
AB = DE Side
3. ABC  DEF
Reasons
1. Given
2. Transitive Prop
3. ASA  ASA
#1
#9
Given: GEH bisects DEF
mD = mF
Prove: GFE  DEH
Statement
1. GEH bisects DEF
mD = mF Angle
2. DE  EF
Side
3. 1 & 2 are vertical
4. 1  2
Angle
5. GFE  DEH
Reasons
1. Given
2. Bisector cut a segment into 2 
parts.
3. Intersect lines form vertical 
4. Vertical  are 
5. ASA  ASA
#10
Given: PQ bisects RS at M
R  S
Prove: RMQ  SMP
Statement
1. PQ bisects RS at M
R  S Angle
2. RM  MS Side
Reasons
1. Given
2. Bisector cut a segment into 2 
#1
3. 1 & 2 are vertical angles
4. 1  2
Angle
5. RMQ  SMP
parts
3. Intersect lines form vertical 
4. Vertical  are 
5. ASA  ASA
#11
Given: DE  DG
EF  GF
Prove: DEF  DFG
Statement
1. DE  DG Side
EF  GF Side
2. DF  DF Side
3. DEF  DFG
Reasons
1. Given
2. Reflexive Post
3. SSS  SSS
#12
Given: KM bisects LKJ
LK  JK
Prove: JKM  LKM
Statement
1. KM bisects LKJ
LK  JK Side
2. 1  2
Angle
Reasons
1. Given
2. An  bisectors cuts the  into
2  parts
#1
3. KM  KM Side
4. JKM  LKM
3. Reflexive Post
4. SAS  SAS
#13
Given: . PR  QR
P  Q
RS is a median
Prove: PSR  QSR
Statement
1. PR  QR
Side
P  Q
Angle
RS is a median
Side
2. PS  SQ
3. PSR  QSR
Reasons
1. Given
2. A median cuts the side into
2  parts
3. SAS  SAS
#14
Given: EG is  bisector
EG is an altitude
Prove: DEG  GEF
Statement
1. EG is  bisector
EG is an altitude
2. 3  4 Angle
Reasons
1. Given
2. An  bisector cuts an  into
2  parts.
#1
3. EG  DF
4. 1 & 2 are rt 
5. 1  2
Angle
6. GE  GE
Side
7. DEG  GEF
3.
4.
5.
6.
7.
An altitude form  lines.
 lines form right angles.
All right angles are 
Reflexive Post
ASA  ASA
#15
Given:
AE
AB
Prove:
1.
2.
3.
4.
5.
6.
Statement
A and D are a rt 
AE  DF
Side
AB  CD
A  D Angle
BC  BC
AB + BC  CD + BC
or AC  BD
Side
AEC  DFB
EC  FB
A and D are a rt 
 DF
 CD
EC  FB
Reasons
1. Given
2. All right angles are .
3. Reflexive Post.
4. Addition Prop.
5. SAS  SAS
6. Corresponding parts of   are .
#16
Given: CA  CB
D midpoint of AB
Prove: A  B
Statement
1. CA  CB Side
D midpoint of AB
Reasons
1. Given
#1
2. AD  DB
Side
3. CD  CD
Side
4. ADC  DBC
5. A  B
2. A midpoint cuts a segment into
2  parts
3. Reflexive Post
4. SSS SSS
5. Corresponding parts of   are .
#17
Given: . AB  CD
CAB  ACD
Prove: AD  CB
1.
2.
3.
4.
Statement
AB  CD Side
CAB  ACD
Angle
AC  AC
Side
ACD  ABC
AD  CB
Reasons
1. Given
2. Reflexive Post
3. SAS SAS
4. Corresponding parts of   are .
#18
Given: AEB & CED bisect each
Other
Prove: C  D
Statement
1. AEB & CED bisect each other
2. CE  ED Side & AE  EB Side
3. 1 and 2 are vertical
Reasons
1. Given
2. A bisector cuts segments into
2  parts.
3. Intersect lines form vertical 
#1
4. 1  2 Angle
5. AEC  DEB
6. C  D
4. Vertical  are 
5. SAS  SAS
6. Corresponding parts of   are
#19
Given: KLM & NML are rt 
KL  NM
Prove: K  N
1.
2.
3.
4.
5.
Statement
KLM & NML are rt 
KL  NM
Side
KLM  NML Angle
LM  LM
Side
KLM  LNM
K  N
Reasons
1. Given
2.
3.
4.
5.
All rt  are 
Reflexive Post.
SAS  SAS
Corresponding parts of   are .
#20
Given: AB  BC
PA  PD
Prove: a) APB
b) APC
Statement
1. AB  BC  CD Side
PA  PD Side & PB  PC Side
2. ABP  CDP
3. APB  DPC
 CD
& PB  PC
 DPC
 DPB
Reasons
1. Given
2. SSS  SSS
3. Corresponding parts of   are .
#1
4. BPC  BPC
5. APB + BPC  DPC + BPC
or APC  DPB
4. Reflexive Post.
5. Addition Prop.
#21
Given: PM is Altitude
PM is median
Prove: a) LNP is isosceles
b) PM is  bisector
1.
2.
3.
4.
5.
Statement
PM is Altitude & PM is median
PM  LN
1 and 2 are rt 
1  2
LM  MN
6. PM  PM
7. LMP  PMN
8. PL  PN
9. LNP is isosceles
10. LPN  MPN
11. PM is  bisector
#22
Reasons
1. Given
2. An altitude form  lines.
3.  lines form right angles.
4. All right angles are 
5. A median cuts the side into
2  parts
6. Reflexive Post.
7. SAS  SAS
8. Corresponding parts of   are .
9. An Isosceles  is a  with2  sides
10.Corresponding parts of   are .
11. A  bisector cuts an  into
2  parts
#1
Given: CA  CB
Prove: CAD  CBE
Statement
1. CA  CB
2. 2  3
3. 1 & 2 are supplementary
3 & 4 are supplementary
4. 1  4 or CAD  CBE
Reasons
1. Given
2. If 2 sides are  then the  opposite
are .
3. Supplementary  are form by a
linear pair.
4. Supplement of   are .
#23
Given: AB  CB & AD  CD
Prove: BAD  BCD
Statement
1. AB  CB & AD  CD
2. 1  2
3  4
3. 1 + 3  2 + 4
or BAD  BCD
#24
Reasons
1. Given
2. If 2 sides are  then the  opposite
are .
3. Addition Post.
#1
Given: ΔABC  ΔDEF
M is midpoint of AB
N is midpoint DE
Prove: ΔAMC  ΔDNF
1.
2.
3.
4.
Statement
ΔABC  ΔDEF
M is midpoint of AB
N is midpoint DE
D  A Angle and DF  AC Side
AM  MB and DN  NE Side
5. ΔAMC  ΔDNF
Reasons
1. Given
2. Given
3. Corresponding parts of  Δ are 
4. A midpoint cuts a segment into
2  parts
5. SAS  SAS
#25
Given: ΔABC  ΔDEF
CG bisects ACB
FH bisects DFE
Prove: CG  FH
Statement
1. ΔABC  ΔDEF
CG bisects ACB
FH bisects DFE
Reasons
#1
#26
Given: ΔAME  ΔBMF
DE  CF
Prove: AD  BC
1.
2.
3.
4.
5.
Statement
ΔAME  ΔBMF
DE  CF
EM  MF
AM  MB Side
1  2 Angle
DE + EM  CF + MF
or DM  MC Side
ΔADM  ΔBCM
AD  BC
Reasons
1. Given
2. Corresponding parts of  Δ are 
3. Addition Post.
4. SAS  SAS
5. Corresponding parts of  Δ are 
Given: AEC & DEB bisect each
other
Prove: E is midpoint of FEG
Statement
1. AEC & DEB bisect each other
Reasons
1. Given
#1
2. DE  BE Side and AE  EC Side
3. AEB & DEC are vertical 
4. AEB  DEC Angle
5. ΔAEB  ΔDEC
6. D  B
7. 1 & 2 are vertical angles
8. 1  2
9. ΔGEB  ΔDEF
10. GE  FE
11. E is midpoint of FEG
2. A bisector cuts a segment into
2  parts.
3. Intersecting lines form vertical 
4. Vertical  are .
5. SAS  SAS
6. Corresponding parts of  Δ are 
7. Intersecting lines form vertical 
8. Vertical  are .
9. ASA  ASA
10. Corresponding parts of  Δ are 
11. A midpoint divides a segment
into 2  parts.
#28
Given: BC  BA
BD bisects CBA
Prove: DB bisects CDA
Statement
Reasons
#1
1. BC  BA Side
BD bisects CBA
2. 1  2 Angle
3.
4.
5.
6.
BD  BD
Side
ΔABD  ΔBCD
3  4
DB bisects CDA
1. Given
2. A bisector cuts an angle into
2  parts.
3. Reflexive Post.
4. SAS  SAS
5. Corresponding parts of  Δ are 
6. A angle bisector cuts an angle
into 2  parts.
#29
Given: AE  FB
DA  CB
A and B are Rt. 
Prove: ADF  CBE
DF  CE
Statement
1. AE  FB
DA  CB Side
A and B are Rt. 
2. EF  EF
3. AE + EF  FB + EF
or AF  EB Side
Reasons
1. Given
2. Reflexive Post
3. Addition Property
#1
4. A  B Angle
5. ADF  CBE
6. DF  CE
4. All rt.  are .
5. SAS  SAS
6. Corresponding parts of  Δ are 
#30
Given: SPR  SQT
PR  QT
Prove: SRQ  STP
R  T
1.
2.
3.
4.
5.
Statement
SPR  SQT Side
PR  QT
S  S Angle
SPR – PR  SQT – QT
or SR  ST Side
SRQ  STP
R  T
Reasons
1. Given
2. Reflexive Post
3. Subtraction Property
4. SAS  SAS
5. Corresponding parts of  Δ are 
#31
Given: DA  CB
DA  AB & CB  AB
Prove: DAB  CBA
AC  BD
1.
2.
3.
4.
5.
6.
Statement
DA  CB Side
DA  AB & CB  AB
DAB and CBA are rt 
DAB  CBA Angle
AB  AB Side
DAB  CBA
AC  BD
Reasons
1. Given
2.
3.
4.
5.
6.
 lines form rt .
All rt  are .
Reflexive post.
SAS  SAS
Corresponding parts of  Δ are .
#1
#32
Given: BAE  CBF
BCE  CDF
AB  CD
Prove: AE  BF
E  F
1.
2.
3.
4.
5.
Statement
BAE  CBF Angle
BCE  CDF Angle
AB  CD
BC  BC
AB + BC  CD + BC
or AC  BD Side
AEC  BDF
AE  BF
E  F
Reasons
1. Given
2. Reflexive Post.
3. Addition Property.
4. ASA  ASA
5. Corresponding parts of  Δ are .
#33
Given: TM  TN
M is midpoint TR
N is midpoint TS
Prove: RN  SM
Statement
Reasons
#1
1. TM  TN Side
M is midpoint TR
N is midpoint TS
2. T  T Angle
3. RM is ½ of TR
NS is ½ of TS
4. RM  NS
5. TM + RM  TN + NS
or RT  TS Side
6. RTN  MTS
7. RN  SM
1. Given
2. Reflexive Post.
3. A midpoint cuts a segment in .
4. ½ of  parts are .
5. Addition Property
6. SAS  SAS
7. Corresponding parts of  Δ are .
#34
Given: AD  CE & DB  EB
Prove: ADC  CEA
Statement
1. AD  CE & DB  EB Side
Reasons
1. Given
#1
2. B  B Angle
3. AD + DB  CE + EB
or AB  BC Side
4. ABE  BCD
5. 1  2
6. 1 & 3 are supplementary
2 & 4 are supplementary
7. 3  4 or
ADC  CEA
2. Reflexive Post
3. Addition Post.
4. SAS  SAS
5. Corresponding parts of  Δ are .
6. A st. line forms supplementary .
7. Supplements of   are .
#35
Given: AE  BF & AB  CD
ABF is the suppl. of A
Prove: AEC  BFD
Statement
1. AE  BF Side & AB  CD
ABF is the suppl. of A
Reasons
1. Given
#1
2. A  1 Angle
3. BC  BC
4. AB + BC  CD + BC
or AC  BD Side
5. AEC  BFD
2. Supplements of   are .
3. Reflexive Post.
4. Addition Property.
5. SAS  SAS
#36
Given: AB  CB
BD bisects ABC
Prove: AE  CE
Statement
1. AB  CB Side
BD bisects ABC
2. 1  2
Angle
3. BE  BE Side
4. BEC  BEA
5. AE  CE
Reasons
1. Given
2. A bisector cuts an  into
2  parts.
3. Reflexive Post.
4. SAS  SAS
5. Corresponding parts of  Δ are 
#37
Given: PB  PC
Prove: ABP  DCP
Statement
1. PB  PC
Reasons
1. Given
#1
2. 1  2
3. 1 & ABP are supplementary
2 & DCP are supplementary
4. ABP  DCP
2.  opposite  sides are .
3. Supplementay  are formed by a
linear pair.
4. Supplements of   are .
#38
Given: AC and BD are  bisectors of
each other.
Prove: AB  BC  CD  DA
1.
2.
3.
4.
Statement
AC and BD are  bisectors of
each other
1, 2, 3 and 4 are rt 
1  2  3  4 Angle
AE  EC and BE  DE 2 sides
5. ABE  BEC  DEC  AED
6. AB  BC  CD  DA
Reasons
1. Given
2.  lines form rt .
3. All rt  are .
4. A bisector cuts a segment into
2  parts.
5. SAS  SAS
6. Corresponding parts of  Δ are 
#39
Given: AEFB, 1  2
CE  DF, AE  BF
Prove: AFD  BEC
Statement
Reasons
#1
1. AEFB, 1  2 Angle
CE  DF Side, AE  BF
2. EF  EF
3. AE + EF  BF + EF or
AF  EB Side
4. AFD  BEC
1. Given
2. Reflexive Post.
3. Addition Property
4. SAS  SAS
#40
Given: SX  SY, XR  YT
Prove: RSY  TSX
1.
2.
3.
4.
Statement
SX  SY Side, XR  YT
SX + XR  SY + YT
or SR  ST Side
S  S
Angle
RSY  TSX
Reasons
1. Given
2. Addition Post.
3. Reflexive Post.
4. SAS  SAS
#41
Given: DA  CB
DA  AB, CB  AB
Prove: DAB  CBA
#1
1.
2.
3.
4.
5.
Statement
DA  CB Side
DA  AB, CB  AB
DAB and CBA are rt. 
DAB  CBA Angle
AB  AB
Side
DAB  CBA
Reasons
1. Given
2.
3.
4.
5.
 lines form rt 
All rt.  are 
Reflexive Post.
SAS  SAS
#42
Given: AF  EC
1  2, 3  4
Prove: ABE  CDF
Statement
1. AF  EC
1  2, 3  4 Angle
2. DFC  BEA
Angle
3. EF  EF
4. AF + EF  EC + EF or
AE  FC Side
5. ABE  CDF
#43
Reasons
1. Given
2. Supplements of   are 
3. Reflexive post.
4. Addition Post.
5. AAS  AAS
#1
Given: AB  BF, CD  BF
1  2, BD  FE
Prove: ABE  CDF
1.
2.
3.
4.
5.
6.
Statement
AB  BF, CD  BF
1  2 Side , BD  FE
B and CDF are rt. 
B  CDF Angle
DE  DE
BD + DE  FE + DE or
BE  DF Side
ABE  CDF
Reasons
1. Given
2.
3.
4.
5.
 lines form rt. 
All rt.  are 
Reflexive Post.
Addition Post.
6, ASA  ASA
#44
Given: BAC  BCA
CD bisects BCA
AE bisects BAC
Prove: ADC  CEA
1.
2.
3.
4.
5.
Statement
BAC  BCA Angle
CD bisects BCA
AE bisects BAC
ECA  ½BAC and
DCA  ½BCA
ECA  DCA Angle
AC  AC
Side
ADC  CEA
Reasons
1. Given
2.  bisector cuts an  in ½
3. ½ of   are 
4. Reflexive post.
5. ASA  ASA
#1
#45
Given: TR  TS, MR  NS
Prove: RTN  STM
Statement
1. TR  TS Side, MR  NS
2, TR – MR  TS – NS or
TM  TN Side
3. T  T Angle
4. RTN  STM
#46
Reasons
1. Given
2. Subtraction Post.
3. Reflexive Post.
4. ASA  ASA
Given: CEA  CDB, ABC
AD and BE intersect at P
PAB  PBA
Prove: PE  PD
Statement
1. CEA  CDB, ABC
AD and BE intersect at P
PAB  PBA
2.
Reasons
1. Given
#1
#47
Given: AB  AD and BC  DC
Prove: 1  2
1.
2.
3.
4.
5.
6.
7.
Statement
AB  AD and BC  DC
AC  AC
ABC  ADC
AE  AE
BAE  DAE
ABE  ADE
1  2
Reasons
1.
2.
3.
4.
5.
6.
7.
Given
Reflexive Post.
SSS  SSS
Reflexive Post.
Corresponding parts of  Δ are .
SAS  SAS
Corresponding parts of  Δ are .
#48
Given: BD is both median and
altitude to AC
Prove: BA  BC
1.
2.
3.
4.
5.
6.
Statement
BD is both median and
altitude to AC
AD  CD Side
ADB and  CDB are rt. 
ADB   CDB Angle
BD  BD
Side
ABD  CBD
Reasons
1. Given
2. A median cuts a segment into 2 
parts
3.  Lines form rt. 
4. All rt.  are 
5. Reflexive Post.
#1
7. BA  BC
6. SAS  SAS
7. Corresponding parts of  Δ are .
#49
Given: CDE  CED and AD  EB
Prove: ACC  BCE
1.
2.
3.
4.
5.
Statement
CDE  CED and AD  EB Side
CDA  CEB Angle
CD  CE Side
ADC  BEC
ACD  BCE
Reasons
1.
2.
3.
4.
5.
Given
Supplements of   are .
Sides opp.   in a  are 
SAS  SAS
Corresponding parts of  Δ are .
#50
Given: Isosceles triangle CAT
CT  AT and ST bisects CTA
Prove: SCA  SAC
1.
2.
3.
4.
Statement
Isosceles triangle CAT
CT  AT Side and ST bisects CTA
CTS  ATS Angle
ST  ST Side
CST  AST
Reasons
1. Given
2. An  bisector cuts an  into 2 
parts
3. Reflexive Post.
4. SAS  SAS
#1
5. CS  AS
6. SCA  SAC
5. Corresponding parts of  Δ are .
6.  opp.  sides in a  are 
#51
Given: 1  2
DB  AC
Prove: ABD  CBD
1.
2.
3.
4.
5.
6.
Statement
1  2 and DB  AC
DBA and DBC are rt. 
DBA  DBC Angle
DAB  DCA Angle
DB  DB Side
ABD  CBD
Reasons
1.
2.
3.
4.
5.
6.
Given
 lines form rt. 
All rt.  are 
Supplements of   are 
Reflexive Post.
AAS  AAS
#52
Given: P  S
R is midpoint of PS
Given: PQR  STR
Statement
1. P  S Angle
R is midpoint of PS
2. PR  RS Side
3. QRP and TRS are vertical 
Reasons
1. Given
2. A midpoint cuts a segment into 2 
parts
3. Intersecting lines form vert. 
#1
4. QRP  TRS
5. PQR  STR
Angle
4. Vertical  are 
5. ASA  ASA
#53
Given: FG  DE
G is midpoint of DE
Given: DFG  EFG
Statement
1. FG  DE
G is midpoint of DE
2. FGD and FGE are rt. 
3. FGD  FGE Angle
4. FG  FG Side
5. DG  GE
Side
6. DFG  EFG
Reasons
1. Given
2.  lines form rt. 
3. All rt.  are 
4. Reflexive Post.
5. A midpoint cuts a segment into 2 
parts.
6. SAS  SAS
#54
Given: AC  CB
D is midpoint of AB
Prove: ACD  BCD
Statement
1. AC  CB Side
D is midpoint of AB
Reasons
1. Given
#1
2. AD  DB
Side
3. CD  CD Side
4. ACD  BCD
2. A midpoint cuts a segment into 2 
parts.
3. Reflexive Post.
4. SSS  SSS
#55
Given: PT bisects QS
PQ  QS and TS  QS
Prove: PQR  RST
Statement
1. PT bisects QS
PQ  QS and TS  QS
2. QR  RS
Side
3. PRQ and TRS are vertical 
4. PRQ  TRS Angle
5. Q and S are rt. 
6. Q  S
Angle
7. PQR  RST
Reasons
1. Given
2. A bisector cuts a segment into 2 
parts.
3. Intersecting lines form vert. 
4. All vert.  are 
5.  lines form rt. 
6. All rt.  are 
7. ASA  ASA
#56
Given: AB  ED and FE  CB
FE  AD and CB  AD
Prove: AEF  CBD
Statement
1. AB  ED and FE  CB Side
Reasons
1. Given
#1
FE  AD and CB  AD
2. BE  BE
3. AB + BE  ED + BE or
AE  DB Side
4. AEF and  DBF are rt. 
5. AEF   DBF Angle
6. AEF  CBD
#57
2. Reflexive Post.
3. Addition Post.
4.  lines form rt. 
5. All rt.  are 
6. SAS  SAS
Given: SM is  bisector of LP
RM  MQ
a  b
Prove: RLM  QPM
1.
2.
3.
4.
Statement
SM is  bisector of LP
RM  MQ Side
a  b
SML and SMP are rt. 
1  2 Angle
LM  PM Side
5. RLM  QPM
Reasons
1. Given
2.  lines form rt. 
3. Complements of   are 
4. A bisector cuts a segment into 2 
parts.
5. SAS  SAS
#59
Given: AC  BC
CD  AB
Prove: ACD  BCD
Statement
Reasons
#1
1. AC  BC
CD  AB
2. CDA and CDB are rt. 
3. CDA  CDB
4. CD  CD
5. ACD  BCD
1. Given
2.
3.
4.
5.
 lines form rt. 
All rt.  are 
Reflexive Post.
SAS  SAS
#60
Given: FQ bisects AS
A  S
Prove: FAT  QST
Statement
1. FQ bisects AS
A  S Angle
2. AT  ST Side
3. ATF & STQ are vertical 
4. ATF  STQ Angle
5. FAT  QST
Reasons
1. Given
2. A bisector cuts a segment into 2 
parts.
3. Intersecting lines form vert. 
4. All vert.  are 
5. ASA  ASA
#61
Given: A  D and BCA  FED
AE  CD
AEF  BCD
Prove: ABC  DFE
Statement
1. A  D Angle and
BCA  FED Angle
Reasons
1. Given
#1
AE  CD and AEF  BCD
2. EC  EC
3. AE + EC  CD + EC or
AC  DE Side
4. ABC  DFE
2. Reflexive Post.
3. Addition Post.
4. ASA  ASA
#62
Given: SU  QR, PS  RT
TSU  QRP
Prove: PQR  STU
Q  U
1.
2.
3.
4.
5.
Statement
SU  QR, PS  RT
TSU  QRP
SR  SR
PS + SR = RT + SR or
PR  TS
PQR  STU
Q  U
#63
Reasons
1. Given
2. Reflexive Post.
3. Addition Post
4. SAS  SAS
5. Corresponding parts of  Δ are .
#1
Given: M  D
ME  HD
THE  SEM
Prove: MTH  DSE
1.
2.
3.
4.
5.
Statement
M  D Angle, ME  HD
THE  SEM
HE  HE
ME – HE  HD - HE or
MH  DE Side
THM  SED Angle
MTH  DSE
Reasons
1. Given
2. Reflexive post.
3. Subtraction Post.
4. Supplements of   are 
5. ASA  ASA
#64
Given; SQ bisects PSR
P  R
Prove: PQS  QSR
Statement
1. SQ bisects PSR
P  R Angle
2. PSQ  RSQ Angle
3. SQ  SQ Side
4. PQS  QSR
Reasons
1. Given
2. an  bisectors cuts an  into 2 
parts.
3. Reflexive Post
4. AAS  AAS
#1
#65
Given: PQ  QS and TS  QS
R midpoint of QS
Prove: P  T
1.
2.
3.
4.
5.
6.
Statement
PQ  QS and TS  QS
R midpoint of QS
Q and S are rt. 
Q  S Angle
PRQ and TRS are vertical 
PRQ  TRS Angle
QR  SQ Side
Reasons
1. Given
2.
3.
4.
5.
6.
 lines form rt. 
All rt.  are 
Intersecting lines form vert. 
All vert.  are 
A midpoint cuts a segment into 2 
#1
7. PQR  TSR
8. P  T
parts.
7. ASA  ASA
8. Corresponding parts of  Δ are .
#66
Given: CB  FB, BT  BV
DV  TS, DC  FS
Prove: D  S
1.
2.
3.
4.
5.
6.
7.
Statement
CB  FB, BT  BV
DV  TS, DC  FS Side
BTV  BVT Angle
CB + BT  FB + BV or
CT  FV Side
VT  VT
DV + VT  TS + VT or
DT  SV Side
DCT  SVF
D  S
Reasons
1. Given
2.  opp.  sides in a  are 
3. Addition Post
4.
5.
6.
7.
Reflexive Post.
Addition Post
SAS  SAS
Corresponding parts of  Δ are .
#1
#67
Given: PQ  DE and PB  AE
QA  PE and DB  PE
Prove: D  Q
1.
2.
3.
4.
Statement
PQ  DE Hyp and PB  AE
QA  PE and DB  PE
AB  AB
PB – AB = AE – AB or
PA  EB Leg
QAP and DBA are rt. 
Reasons
1. Given
2. Reflexive post.
3. Subtraction Post.
4.  lines form rt. 
#1
5. QAP  DBA
6. PAQ  EBD
7. D  Q
5. All rt.  are 
6. HL  HL
7. Corresponding parts of  Δ are .
#68
Given: TS  TR
P  Q
Prove: PS  QR
1.
2.
3.
4.
5.
Statement
TS  TR Side
P  Q Angle
PTS and QTR are vertical 
PTS  QTR Angle
PTS  QTR
PS  QR
Reasons
1. Given
2.
3.
4.
5.
Intersecting lines form vert. 
All vert.  are 
AAS  AAS
Corresponding parts of  Δ are .
#69
Given: HY and EV bisect each other
Prove: HE  VY
Statement
1. HY and EV bisect each other
2. HA  YA Side and EA  VA Side
3.
4.
5.
6.
HAE and YAV are vertical 
HAE  YAV Angle
HAE  YAV
HE  VY
Reasons
1. Given
2. A bisector cuts a segment into 2 
parts.
3. Intersecting lines form vert. 
4. All vert.  are 
5. SAS  SAS
6. Corresponding parts of  Δ are .
#1
#70
Given: E  D and A  C
B is the midpoint of AC
Prove: EA  DC
Statement
1. E  D Angle and A  C Angle
B is the midpoint of AC
2. EA  DC Side
3. ABE  CBE
4. EA  DC
Reasons
1. Given
2. A midpoint cuts a segment into 2 
parts.
3. AAS  AAS
4. Corresponding parts of  Δ are .
#71
Given: E is midpoint of AB
DA  AB and CB  AB
1  2
Prove: AD  CB
Statement
1. E is midpoint of AB
DA  AB and CB  AB
1  2
2. AE  EB Side
3. DE  CE Side
Reasons
1. Given
2. A midpoint cuts a segment into 2 
parts.
3.  opp.  sides in a  are 
#1
4. ADE  BCD
5. AD  CB
4. HL  HL
5. Corresponding parts of  Δ are .