SSS/SAS/ASA Proofs. C. !. 1. 2. A. B. D. Quiz Question. W. !. 3. 4. Y. Z. X. !. G. I. H. J. F. K. L. C. !. A. 1. D. 2. B. M. !. R. N. O. !. B. E. C. 1. 2. A. D. Quiz Question. !. N. Q. 4. 5. O. P. M. C. 1. 2. B. A. D. E. G. H. 1. 2. F.
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SSS/SAS/ASAProofs
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Triangle Congruence and Similarity Proofs
Augustus Vitug
Melissa Moize
Sketch
AB AC
BD DC
AD AD
BAD CAD
Statement
Reason
Given
AB AC
BD DC
Prove
BAD CAD
Sketch
ABC DCB
CB BC
DBC ACB
ABC DCB
CA DB
AB CD
Statement
Reason
Given
ABCD
Prove
AC BD
CD AB
Sketch
ABC DCB
CB BC
DBC ACB
ABC DCB
AB CD
ADC BAD
ABE DCF
AE DE
BECE
Statement
Reason
Given
ABCD
Prove
AEDE
BECE
Sketch
ABC DCB
CB BC
ACB DBC
ABC DCB
A D
ABC + DBC DCB +ACB
Statement
Reason
Given
Prove
A D
ABD DCA
Sketch
ABC DCB
CBBC
CBD BCA
ABC DCB
FBD+BFD+BDF ECA+CEA+CAE
BDF CAE
AEFD
ACBD
BFD CEA
CE BF
EF FE
EF+FB FE+EC
EB CF
AB CD
AEFD
CFD BEA
Statement
Reason
Given
ABCD
AEFD
AEC=90
BFD=90
Prove
CFD BEA
Sketch
AC BD
ACD BDC
CD DC
ADC BDC
CE+BE DE+AE
CE DE
CED is isos
Statement
Reason
Given
ABCD is iso.
Prove
CED is isos
Sketch
AB CD
B D
BE DE
BEA DEC
G H
EC EA
FE XE
FEA XEC
AF CX
Statement
Reason
Given
AB CD
B D
E is the midpoint of BD & FX
Prove
AF CX
Sketch
AECE
DEC BEA
BE DE
AEB CED
ABE CDE
ABE,CDE are alt. int. ’s
AB || DC
Statement
Reason
Given
Line AC bis. Line BD
Prove
AB || CD
Sketch
A D
BC FE
B = 90- A E = 90- D
B E
ABC DEF
BA DE
Statement
Reason
Given
ABC is a Right
BC FE
A D
Prove
BA DE
Sketch
AGE+EGB CGF+ FGD
AGB CGD
FGD EGB
ABGCDG
DFG BEG
Statement
Reason
Given
Prove
Sketch
AED BEC
DE CE
ADC-EDC BCD ECD
ADE BCE
ADE BCE
AD BC
ADC BCD
DC CD
ADC BCD
Statement
Reason
Given
EDC is isosceles
Prove
ADC BCD
Sketch
AE BE
AED BEC
DE CE
ADE BCE
FDE GCE
DECE
FED GEC
FD GC
EDC ECD
ADE+EDC BCE+ ECD
ADCBCD
FGDC
Statement
Reason
Given
AEBE
EDC is isosceles
Prove
FG DC
Sketch
AC BD
ACD BDC
CD DC
ACD BDC
AD BC
Statement
Reason
Given
Rectangle ABCD
Prove
AD BC
Sketch
BAM CAM
ABAC
B C
BAM CAM
BM CM
BMA CMA
BMC 180
BMA = 1/2180=90= CMA
AM bis. Of BC
Statement
Reason
Given
ABC w/
AM bis.
ABAC
Prove
AM bis.
Sketch
¾=5/6.6666
AD/AB=AE/AC
A A
ADE ABC
Statement
Reason
Given
DE || BC
Prove
ADE ABC
Sketch
AEBE
BEDAEC
CE DE
AC BD
Statement
Reason
Given
AEBE
CEDE
Prove
AC BD
Sketch
BCA EFD
FC CF
AF CD
AF + FC DC + CF
ABC DEF
Statement
Reason
Given
AF DC
FE || CB
AB || DE
Prove
ABC DEF
Sketch
BG EG
EG + GF=BG+GC
BC EF
FC FC
AF+FC=DC+CF
GFC GCF
AC=CD
ABC DEF
Statement
Reason
Given
FGC Isosceles
AF DC
BG EG
Prove
ABC DEF
Sketch
BM CM
AMB = 90 = AMC
AB AC
B C
BAM CAM
BAM CAM
AM is bis. of A
Statement
Reason
AB AC
AM is
Prove
bis. of BC is bis. Of A
Sketch
BMA=90= CMA
B C
B+ BMA+ BAM=180
C+ CMA+ CAM =180
B+ BMA+ BAM= C+ CMA+ CAM
BAM CAM
AM is bis. of A
Statement
Reason
Given
ABC is isos.
AC AB
AM is Alt.
Prove
Alt. AM is bis. of A
Sketch
AB AC
C B
AMB=90= AMC
BAM CAM
BM CM
Alt. AM is bis. of BC
Statement
Reason
Given
ABC is isos.
AB AC
AM is Alt.
Prove
Alt. AM is bis. of BC
Sketch
ACD BDC
CD DC
CEA DEB
AC BD
C D
CE DE
ACE BED
AE BE
Statement
Reason
Given
Trapezoid ABCD is and isosceles
E is midpoint of CD
Prove
AE BE
Sketch
ABC is a Rt. Triangle
CD is the altitude to hyp.
c/a=a/e
a2=c e
c/b=b/d
b2=cd
a2 + b2 = ce + cd
a2+b2=c2
Statement
Reason
Given
Rt. ABC
Prove
a2+b2=c2
Sketch
DAB CAB
DBA CBA
AB AB
ABD ABC
Statement
Reason
Given
DAB CAB
DBA CBA
Prove
ABD ABC
Sketch
AE FE
AED FEJ
DE JE
ADE FJE
D J
AEB+BEC+CED FEG+GEH+HEJ
CED HEJ
CED HEJ
BEC GEH
CE HE
BCE +DCE=180
GHE +JHE=180
BCE+DCE GHE+ JHE
BCE GHE
BEC GHE
Statement
Reason
Given
AE FE, DE JE
BEC GEH
AEB FEG
Prove
BEC GEH
Sketch
Statement
Reason
Given
Prove