given: abc cd bisects ab cd ab prove: acd bcd · #1 #5 given: aeb & ced intersect at e e is the...
TRANSCRIPT
![Page 1: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/1.jpg)
#1
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 .
5. SAS SAS
![Page 2: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/2.jpg)
#1 #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
![Page 3: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/3.jpg)
#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
![Page 4: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/4.jpg)
#1
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: mA = 50, mB = 45,
AB = 10cm, mD = 50
mE = 45 and DE = 10cm
Prove: ABC DEF
Statement
1. mA = 50, mB = 45,
AB = 10cm, mD = 50
mE = 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
![Page 5: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/5.jpg)
#1 #9
Given: GEH bisects DEF
mD = mF
Prove: GFE DEH
Statement 1. GEH bisects DEF
mD = mF 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
![Page 6: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/6.jpg)
#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
![Page 7: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/7.jpg)
#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.
![Page 8: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/8.jpg)
#1
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
![Page 9: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/9.jpg)
#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
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.
3. Intersect lines form vertical
![Page 10: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/10.jpg)
#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
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
3. Corresponding parts of are .
![Page 11: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/11.jpg)
#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
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
![Page 12: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/12.jpg)
#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
Reasons 1. Given
2. If 2 sides are then the opposite
are . 3. Addition Post.
#24
![Page 13: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/13.jpg)
#1
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
![Page 14: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/14.jpg)
#1
#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
![Page 15: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/15.jpg)
#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
![Page 16: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/16.jpg)
#1
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
![Page 17: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/17.jpg)
#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
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
6. Corresponding parts of Δ are .
![Page 18: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/18.jpg)
#1
#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
![Page 19: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/19.jpg)
#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
![Page 20: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/20.jpg)
#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
![Page 21: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/21.jpg)
#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
![Page 22: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/22.jpg)
#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
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
Statement Reasons
![Page 23: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/23.jpg)
#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
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
![Page 24: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/24.jpg)
#1
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
![Page 25: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/25.jpg)
#1
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 ½BAC and
DCA ½BCA
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
![Page 26: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/26.jpg)
#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
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
![Page 27: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/27.jpg)
#1
#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.
![Page 28: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/28.jpg)
#1
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
![Page 29: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/29.jpg)
#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
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
3. Intersecting lines form vert.
![Page 30: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/30.jpg)
#1
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
![Page 31: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/31.jpg)
#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
![Page 32: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/32.jpg)
#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
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
![Page 33: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/33.jpg)
#1
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
![Page 34: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/34.jpg)
#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
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 .
#63
![Page 35: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/35.jpg)
#1
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
![Page 36: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/36.jpg)
#1 #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
6. A midpoint cuts a segment into 2
![Page 37: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/37.jpg)
#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
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
7. Corresponding parts of Δ are .
![Page 38: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/38.jpg)
#1 #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.
![Page 39: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/39.jpg)
#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
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
6. Corresponding parts of Δ are .
![Page 40: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/40.jpg)
#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
![Page 41: Given: ABC CD bisects AB CD AB Prove: ACD BCD · #1 #5 Given: AEB & CED intersect at E E is the midpoint AEB AC ... 5. Intersect lines form vertical 6. Vertical are 7. ASA ASA #7](https://reader030.vdocuments.net/reader030/viewer/2022040717/5e2336f68a95045a0e35eff2/html5/thumbnails/41.jpg)
#1
4. ADE BCD
5. AD CB
4. HL HL
5. Corresponding parts of Δ are .