#1

Given: ABC

CD bisects AB

CD AB

Prove: ACD BCD

Statement

1. ABC

CD bisects AB

CD AB

Reasons 1. Given

#2

Given: ABC and DBE bisect each other.

Prove: ABD CBD

Statement

Reasons

#3

Given: AB CD and BC AD

DAB, ABC, BCD and CDA

are rt

Prove: ABC ADC

Statement

Reasons

#4

Given: PQR RQS

PQ QS

Prove: PQR RQS

Statement

Reasons

#5

Given: AEB & CED intersect at E

E is the midpoint AEB

AC AE & BD BE

Prove: AEC BED

Statement

Reasons

#6

Given: AEB bisects CED

AC CED & BD CED

Prove: EAC EBD

Statement

Reasons

#7

Given: ABC is equilateral

D midpoint of AB

Prove: ACD BCD

Statement

Reasons

#8

Given: mA = 50, mB = 45,

AB = 10cm, mD = 50

mE = 45 and DE = 10cm

Prove: ABC DEF

Statement

Reasons

#9

Given: GEH bisects DEF

mD = mF

Prove: GFE DEH

Statement

Reasons

#10

Given: PQ bisects RS at M

R S

Prove: RMQ SMP

Statement

Reasons

#11

Given: DE DG

EF GF

Prove: DEF DFG

Statement

Reasons

#12

Given: KM bisects LKJ

LK JK

Prove: JKM LKM

Statement

Reasons

#13

Given: PR QR

P Q

RS is a median

Prove: PSR QSR

Statement

Reasons

#14

Given: EG is bisector

EG is an altitude

Prove: DEG GEF

Statement

Reasons

#15

Given: A and D are a rt

AE DF

AB CD

Prove: EC FB

Statement

Reasons

#16

Given: AC BC

D midpoint of AB

Prove: A B

Statement

Reasons

#17

Given: . AB CD

CAB ACD

Prove: AD BC

Statement

Reasons

#18

Given: AEB & CED bisect each Other

Prove: C D

Statement

Reasons

#19

Given: KLM & NML are rt

KL NM

Prove: K N

Statement

Reasons

#20

Given: AB BC CD

PA PD & PB PC

Prove: a) APB DPC

b) APC DPB

Statement

Reasons

#21

Given: PM is Altitude

PM is median

Prove: a) LNP is isosceles

b) PM is bisector

Statement

Reasons

#22

Given: AC BC

Prove: CAD CBE

Statement

Reasons

#23

Given: AB BC & AD CD

Prove: BAD BCD

Statement

Reasons

#24

Given: ΔABC ΔDEF

M is midpoint of AB

N is midpoint DE

Prove: ΔAMC ΔDNF

Statement

Reasons

#25

Given: ΔABC ΔDEF

CG bisects ACB

FH bisects DFE

Prove: CG FH

Statement

Reasons

#26

Page187#6

Given: ΔAME ΔBMF

DE CF

Prove: AD BC

Statement

Reasons

#27

Given: AEC & DEB bisect each other

Prove: E is midpoint of FEG

Statement

Reasons

#28

Given: BC BA

BD bisects CBA

Prove: BD bisects CDA

Statement

Reasons

#29

Given: AE FB

AD BC

A and B are Rt.

Prove: ADF CBE

DF CE

Statement

Reasons

#30

Given: SPR SQT

PR QT

Prove: SRQ STP

R T

Statement

Reasons

#31

Given: AD BC

AD AB & BC AB

Prove: DAB CBA

AC BD

Statement

Reasons

#32

Given: BAE CBF

BCE CDF

AB CD

Prove: AE BF

E F

Statement

Reasons

#33

Given: TM TN

M is midpoint TR

N is midpoint TS

Prove: RN SM

Statement

Reasons

#34

Given: AD CE & BD EB

Prove: ADC CEA

Statement

Reasons

#35

Given: AE BF & AB CD

ABF is the suppl. of A

Prove: AEC BFD

Statement

Reasons

#36

Given: AB BC

BD bisects ABC

Prove: AE CE

Statement

Reasons

#37

Given: PB PC

Prove: ABP DCP

Statement

Reasons

#38

Given: AC and BD are bisectors of each other.

Prove: AB BC CD AD

Statement

Reasons

#39

Given: AEFB, 1 2

CE DF , AE BF

Prove: AFD BEC

Statement

Reasons

#40

Given: SX SY , XR YT

Prove: RSY TSX

Statement

Reasons

#41

Given: AD BC

AD AB , BC AB

Prove: DAB CBA

Statement

Reasons

#42

Given: AF CE

1 2, 3 4

Prove: ABE CDF

Statement

Reasons

#43

Given: AB BF , CD BF

1 2, BD FE

Prove: ABE CDF

Statement

Reasons

#44

Given: BAC BCA

CD bisects BCA

AE bisects BAC

Prove: ADC CEA

Statement

Reasons

#45

Given: TR TS , MR NS

Prove: RTN STM

Statement

Reasons

#46

Given: CEA CDB, ABC

AD and BE intersect at P

PAB PBA

Prove: PE PD

Statement 1.

Reasons

#47

Given: AB AD and BC CD

Prove: 1 2

Statement

Reasons

#48

Given: BD is both median and altitude to AC

Prove: BA BC

Statement

Reasons

#49

Given: CDE CED and AD EB

Prove: ACD BCE

Statement

Reasons

#50

Given: Isosceles triangle CAT

CT AT and ST bisects CTA

Prove: SCA SAC

Statement

Reasons

#51

Given: 1 2

BD AC

Prove: ABD CBD

Statement

Reasons

#52

Given: P S

R is midpoint of PS

Given: PQR STR

Statement

Reasons

#53

Given: FG DE

G is midpoint of DE

Given: DFG EFG

Statement

Reasons

#54

Given: AC BC

D is midpoint of AB

Prove: ACD BCD

Statement

Reasons

#55

Given: PT bisects QS

PQ QS and TS QS

Prove: PQR RST

Statement

Reasons

#56

Given: AB DE and FE BC

FE AD and BC AD

Prove: AEF CBD

Statement

Reasons

#57

Given: SM is bisector of LP

RM MQ

a b

Prove: RLM QPM

Statement

Reasons

#59

Given: AC BC

CD AB

Prove: ACD BCD

Statement

Reasons

#60

Given: FQ bisects AS

A S

Prove: FAT QST

Statement

Reasons

#61

Given: A D and BCA FED

AE CD

AEF BCD

Prove: ABC DFE

Statement

Reasons

#62

Given: SU QR , PS RT

TSU QRP

Prove: PQR STU

Q U

Statement

Reasons

#63

Given: M D

ME HD

THE SEM

Prove: MTH DSE

Statement

Reasons

#64

Given; SQ bisects PSR

P R

Prove: PQS QSR

Statement

Reasons

#65

Given: PQ SQ and TS QS

R midpoint of QS

Prove: P T

Statement

Reasons

#66

Given: BC FB , BT BV

DV TS , CD FS

Prove: D S

Statement

Reasons

#67

Given: PQ DE and PB AE

QA PE and BD PE

Prove: D Q

Statement

Reasons

#68

Given: TS TR

P Q

Prove: PS QR

Statement

Reasons

#69

Given: HY and EV bisect each other

Prove: HE VY

Statement

Reasons

#70

Given: E D and A C

B is the midpoint of AC

Prove: AE DC

Statement

Reasons

#71

Given: E is midpoint of AB

AD AB and BC AB

1 2

Prove: AD CB

Statement

Reasons