Given: ABC CD bisects AB CD AB Prove: ACD BCD. Statement 1. ABC CD bisects AB. Reasons. 1. Given

Given: ABC CD bisects AB CD  AB Prove: ACD  BCD Statement 1. ABC CD bisects AB CD  AB 2. AD  DB Side

3. CDA and CDB are right  4. CDA  CDB Angle 5. CD  CD Side

6. ACD  BCD

Reasons 1. Given

2. A bisector cuts a segment into 2  parts.

3.  lines form right . 4. All rt  are .

5. Reflexive post. 6. SAS  SAS

#2

Given: ABC and DBE bisect each other.

Prove: ABD  CBD Statement

1. ABC and DBE bisect each other. 2. AB  BC Side

BD  BE Side

3. ABD and BEC are vertical  4. ABD  BEC Angle

5. ABD  CBD

Reasons 1. Given

2. A bisector cuts a segment into 2  parts.

3. Intersecting lines form vertical . 4. Vertical  are .

#3

Given: AB  CD and BC  DA DAB, ABC, BCD and CDA

are rt 

Prove: ABC  ADC Statement

1. AB  CD Side BC  DA Side

2. DAB, ABC, BCD and CDA are rt 

3. ABC  ADC Angle 4. 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

#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 

5. AEC & DEB are vertical  6. AEC  DEB Angle 7. EAC  EBD

5. Intersect lines form vertical  6. Vertical  are 

7. ASA  ASA #7

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

#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

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

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.

3. EG  DF

4. 1 & 2 are rt  5. 1  2 Angle 6. GE  GE Side 7. DEG  GEF

3. An altitude form  lines. 4.  lines form right angles. 5. All right angles are  6. Reflexive Post

7. ASA  ASA

#15

Given: A and D are a rt  AE  DF

AB  CD Prove: EC  FB

Statement 1. A and D are a rt  AE  DF Side AB  CD 2. A  D Angle 3. BC  BC 4. AB + BC  CD + BC or AC  BD Side 5. AEC  DFB 6. 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

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 Statement 1. AB  CD Side

CAB  ACD Angle 2. AC  AC Side 3. ACD  ABC 4. 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.

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 Statement 1. KLM & NML are rt  KL  NM Side 2. KLM  NML Angle 3. LM  LM Side 4. KLM  LNM 5. K  N Reasons 1. Given 2. All rt  are  3. Reflexive Post. 4. SAS  SAS

5. Corresponding parts of   are .

#20 Given: AB  BC  CD PA  PD & PB  PC Prove: a) APB  DPC b) APC  DPB Statement 1. AB  BC  CD Side

PA  PD Side & PB  PC Side 2. ABP  CDP

3. APB  DPC

Reasons 1. Given

2. SSS  SSS

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 Statement

1. PM is Altitude & PM is median 2. PM  LN 3. 1 and 2 are rt  4. 1  2 5. LM  MN 6. PM  PM 7. LMP  PMN 8. PL  PN 9. LNP is isosceles 10. LPN  MPN 11. PM is  bisector 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 #22

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 Reasons 1. Given

2. If 2 sides are  then the  opposite are .

3. Addition Post.

Given: ΔABC  ΔDEF M is midpoint of AB N is midpoint DE Prove: ΔAMC  ΔDNF Statement 1. ΔABC  ΔDEF 2. M is midpoint of AB N is midpoint DE

3. D  A Angle and DF  AC Side 4. 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

#26 Given: ΔAME  ΔBMF DE  CF Prove: AD  BC Statement 1. ΔAME  ΔBMF DE  CF 2. EM  MF AM  MB Side 1  2 Angle 3. DE + EM  CF + MF or DM  MC Side 4. ΔADM  ΔBCM 5. 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

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

1. BC  BA Side BD bisects CBA 2. 1  2 Angle 3. BD  BD Side 4. ΔABD  ΔBCD 5. 3  4 6. 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

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 Statement 1. SPR  SQT Side PR  QT 2. S  S Angle 3. SPR – PR  SQT – QT or SR  ST Side 4. SRQ  STP 5. 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 Statement

1. DA  CB Side

DA  AB & CB  AB 2. DAB and CBA are rt  3. DAB  CBA Angle 4. AB  AB Side 5. DAB  CBA 6. AC  BD Reasons 1. Given 2.  lines form rt . 3. All rt  are . 4. Reflexive post. 5. SAS  SAS

#32 Given: BAE  CBF BCE  CDF AB  CD Prove: AE  BF E  F Statement 1. BAE  CBF Angle BCE  CDF Angle AB  CD 2. BC  BC 3. AB + BC  CD + BC or AC  BD Side 4. AEC  BDF 5. 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. 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

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

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

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

Statement

1. AC and BD are  bisectors of each other

2. 1, 2, 3 and 4 are rt  3. 1  2  3  4 Angle 4. 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

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 Statement 1. SX  SY Side, XR  YT 2. SX + XR  SY + YT or SR  ST Side 3. S  S Angle 4. 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

Statement 1. DA  CB Side

DA  AB, CB  AB

2. DAB and CBA are rt.  3. DAB  CBA Angle 4. AB  AB Side 5. DAB  CBA Reasons 1. Given 2.  lines form rt  3. All rt.  are  4. Reflexive Post. 5. 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 Reasons 1. Given 2. Supplements of   are  3. Reflexive post. 4. Addition Post. 5. AAS  AAS #43

Given: AB  BF, CD  BF 1  2, BD  FE Prove: ABE  CDF Statement 1. AB  BF, CD  BF 1  2 Side , BD  FE 2. B and CDF are rt.  3. B  CDF Angle 4. DE  DE 5. BD + DE  FE + DE or BE  DF Side 6. ABE  CDF Reasons 1. Given 2.  lines form rt.  3. All rt.  are  4. Reflexive Post. 5. Addition Post. 6, ASA  ASA #44

Given: BAC  BCA CD bisects BCA AE bisects BAC Prove: ADC  CEA

Statement 1. BAC  BCA Angle CD bisects BCA AE bisects BAC 2. ECA  ½BAC and DCA  ½BCA

3. ECA  DCA Angle 4. AC  AC Side 5. ADC  CEA Reasons 1. Given 2.  bisector cuts an  in ½ 3. ½ of   are  4. Reflexive post. 5. ASA  ASA

#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 Reasons 1. Given 2. Subtraction Post. 3. Reflexive Post. 4. ASA  ASA #46

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

#47 Given: AB  AD and BC  DC Prove: 1  2 Statement 1. AB  AD and BC  DC 2. AC  AC 3. ABC  ADC 4. AE  AE 5. BAE  DAE 6. ABE  ADE 7. 1  2 Reasons 1. Given 2. Reflexive Post. 3. SSS  SSS 4. Reflexive Post.

5. Corresponding parts of  Δ are . 6. SAS  SAS

7. Corresponding parts of  Δ are .

#48

Given: BD is both median and altitude to AC Prove: BA  BC

Statement 1. BD is both median and

altitude to AC 2. AD  CD Side

3. ADB and  CDB are rt.  4. ADB   CDB Angle 5. BD  BD Side

6. 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.

7. BA  BC 6. SAS  SAS

7. Corresponding parts of  Δ are . #49

Given: CDE  CED and AD  EB Prove: ACC  BCE

Statement

1. CDE  CED and AD  EB Side 2. CDA  CEB Angle

3. CD  CE Side 4. ADC  BEC 5. ACD  BCE Reasons 1. Given 2. Supplements of   are . 3. Sides opp.   in a  are  4. SAS  SAS

5. Corresponding parts of  Δ are . #50

Given: Isosceles triangle CAT

CT  AT and ST bisects CTA Prove: SCA  SAC

Statement 1. Isosceles triangle CAT

CT  AT Side and ST bisects CTA 2. CTS  ATS Angle

3. ST  ST Side 4. CST  AST

Reasons 1. Given

2. An  bisector cuts an  into 2  parts

3. Reflexive Post. 4. SAS  SAS

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 Statement 1. 1  2 and DB  AC 2. DBA and DBC are rt.  3. DBA  DBC Angle 4. DAB  DCA Angle 5. DB  DB Side 6. ABD  CBD Reasons 1. Given 2.  lines form rt.  3. All rt.  are  4. Supplements of   are  5. Reflexive Post. 6. 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

4. QRP  TRS Angle

5. PQR  STR 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

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

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 2. Reflexive Post. 3. Addition Post. 4.  lines form rt.  5. All rt.  are  6. SAS  SAS #57 Given: SM is  bisector of LP RM  MQ a  b Prove: RLM  QPM Statement 1. SM is  bisector of LP RM  MQ Side a  b 2. SML and SMP are rt.  3. 1  2 Angle 4. 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. AC  BC CD  AB

2. CDA and CDB are rt.  3. CDA  CDB 4. CD  CD 5. ACD  BCD 1. Given 2.  lines form rt.  3. All rt.  are  4. Reflexive Post. 5. 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

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 Statement 1. SU  QR, PS  RT TSU  QRP 2. SR  SR 3. PS + SR = RT + SR or PR  TS 4. PQR  STU 5. Q  U Reasons 1. Given 2. Reflexive Post. 3. Addition Post 4. SAS  SAS

5. Corresponding parts of  Δ are .

Given: M  D ME  HD THE  SEM Prove: MTH  DSE Statement 1. M  D Angle, ME  HD THE  SEM 2. HE  HE 3. ME – HE  HD - HE or MH  DE Side 4. THM  SED Angle 5. 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

#65 Given: PQ  QS and TS  QS R midpoint of QS Prove: P  T Statement 1. PQ  QS and TS  QS R midpoint of QS 2. Q and S are rt.  3. Q  S Angle

4. PRQ and TRS are vertical  5. PRQ  TRS Angle 6. QR  SQ Side Reasons 1. Given 2.  lines form rt.  3. All rt.  are 

4. Intersecting lines form vert.  5. All vert.  are 

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 Statement 1. CB  FB, BT  BV DV  TS, DC  FS Side 2. BTV  BVT Angle 3. CB + BT  FB + BV or CT  FV Side 4. VT  VT 5. DV + VT  TS + VT or DT  SV Side 6. DCT  SVF 7. D  S Reasons 1. Given

2.  opp.  sides in a  are  3. Addition Post

4. Reflexive Post. 5. Addition Post 6. SAS  SAS

#67 Given: PQ  DE and PB  AE QA  PE and DB  PE Prove: D  Q Statement 1. PQ  DE Hyp and PB  AE QA  PE and DB  PE 2. AB  AB 3. PB – AB = AE – AB or PA  EB Leg

4. QAP and DBA are rt. 

Reasons 1. Given

2. Reflexive post. 3. Subtraction Post. 4.  lines form rt. 

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 Statement 1. TS  TR Side P  Q Angle

2. PTS and QTR are vertical  3. PTS  QTR Angle

4. PTS  QTR 5. PS  QR

Reasons 1. Given

2. Intersecting lines form vert.  3. All vert.  are 

4. AAS  AAS

5. 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. HAE and YAV are vertical  4. HAE  YAV Angle

5. HAE  YAV 6. 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

#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.

4. ADE  BCD