sss/sas/asa proofs
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
SSS/SAS/ASAProofs
21
C
A BD
Given: CD AB; 1 2
Prove: ADC BDC
!
Quiz Question
43
W
Y ZX
Given: WX YZ; 3 4
Prove: YXW ZXW
!
HG I
JKF L
Given:
;
Prove:
GKF ILJ
GK IL FL KJ
GF IJ
!
Given: ; 1 2
Prove:
AB AC
B C
1
2
A
C
D
B
!
N R O
MGiven: MR NO;MR bisects NMO
Prove:R is midpoint of NO
!
1 2C
A
B E
D
Given: ; 1 2
Prove:
AC CD
AB ED
!
4 5O
N
M P
Q
Given: ; 4 5
Prove:
NO OQ
MO PO
!Quiz Question
C
BEDA
1 2
Given: ; ;
Prove: 1 2
AC BC AE BD CD CE
H
D
G
B
CE
F 1 2
Given: 1and aresuppplementary
;
Prove: ||
B
BC EG DB HE
GH CD
1 2C
A
B E
D
Given: Cis the midpoint of AE and BD
Prove: 1 2
1 23 4A
B
C
D
E
F
Given: AB||EF; BC||DE; AD CF
Prove: ABC FED
A
XY
12
34
Given: 1 3;AB AC
Prove: ABY ACX
B C
A
XY
12
34
Given: AB AC;AX AY
Prove: 2 4
R
S
U
T12
3
4
X
Given: RS RU; 1 2
Prove: 3 4
D C
A B Y
1 3 4 2
Given: 1 2;AD BC
Prove: AC BD
E
DA
GC
F
B
Given : ABC ADE,DE BC
E and ABCaresupplementary to DCF
Prove: AD bisects EAB
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Q
R S
TP
Given: RP||ST, RQ ST
Prove: S RPT
A
DC
BE
Given: C is the midpoint of BD
AB BD and BD DE
Prove: = ,and that Cisa midpointAC CE
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Quiz Question
Given as homework
CA
B
D
Given: AB BC;Dis midpoint of AC
Prove: BD AC
Hw 11.3
CA
B D
EGiven: E is midpoint of AD and BC
Prove: AB || CD
Hw 11.3
F
ED
A CB
GGiven: F G, FB GB, DG FE, AD CE
Prove: AB CB
Hw 11.4
VT
WR
SU
Given: S V, RS UV, ST VW
Prove: RW UT
Hw 11.4
M S P Q
N R
Given: NM MQ; RQ MQ; MN QR; MS QP
Prove: NP RS
Hw 11.5
CA
B
D
Given: ;
Prove: bisects
AB CB AD CD
BD ABC
Hw 11.5
1 2 3 4
A
B M C
Given: 1 4; AB AC
M is midpoint of BC
Prove: AMB AMC
Hw 11.6
XW
Z Y3
41
2Given: WX YZ; ZW XY
Prove: WX||ZY
QUIZ
Triangle Congruence and Similarity Proofs
Augustus VitugMelissa Moize
Proof Title:
Sketch
• AB AC• BD DC • AD AD• BAD CAD • • • • • • • • • • •
• Given • Given • Reflexive property • SSS• • • • • • • • •
GivenAB ACBD DC
ProveBAD CAD
Statement Reason
Proof Title:
Sketch
• ABC DCB• CB BC• DBC ACB• ABC DCB• CA DB• AB CD• • • • • • • • •
• Alt. Int. ’s • reflexive• Alt. Int. ’s • ASA • CPCTC• CPCTC• • • • • • • •
Given ABCD
ProveAC BDCD AB
Statement Reason
Proof Title: Parallelogram Diagonals Bisect Each Other
Sketch
• ABC DCB• CB BC• DBC ACB• ABC DCB• AB CD• ADC BAD• ABE DCF• AE DE• BECE• • •
• Alt. Int. ’s • Reflexive property • Alt. Int. ’s • ASA• CPCTC • Alt. Int. ’s• ASA • CPCTC• CPCTC• • • • • •
Given
Prove
Statement Reason
ABCD
AEDE
BECE
Proof Title:
Sketch
• ABC DCB• CB BC• ACB DBC• ABC DCB• A D• ABC + DBC DCB +ACB
• • • • • • • • •
• Alt. Int. ’s• reflexive• Alt. Int. ’s• ASA• CPCTC• 2nd Postulate • • • • • • • •
Given
ProveA D
ABD DCA
Statement Reason
Proof Title: Compound Polygon #1
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
• Alt. int. ’s• reflexive property • Alt. int. ’s• ASA • Triangle Sums • Subtraction Property • Given • CPCTC • ASA• CPCTC • Reflexive Property • Sums of equals • Sums of equals• CPCTC • Given • SSS
Given
Prove
Statement Reason
ABCD
AEFD
AEC=90
BFD=90
CFD BEA
Proof Title: Compound # 2
Sketch
• AC BD• ACD BDC• CD DC• ADC BDC• CE+BE DE+AE• CE DE• CED is isos• • • • • • • •
• Given • Def. isos • Reflexive• SAS• Sums of Equals • Subtraction property • def. isos. • • • • • • •
Given
ProveCED is isos
Statement Reason
ABCD is iso.
Proof Title: ?
Sketch
• AB CD• B D• BE DE• BEA DEC• G H• EC EA• FE XE• FEA XEC• AF CX• • • • • • •
• Given • Given• Def. of Midpoint • SAS • CPCTC • CPCTC • Def. of Midpoint • SAS • CPCTC • • • • •
GivenAB CD B DE is the midpoint of
BD & FX
ProveAF CX
Statement Reason
Proof Title: Simple Bowtie
Sketch
• AECE• DEC BEA• BE DE• AEB CED• ABE CDE• ABE,CDE are alt. int. ’s• AB || DC• • • • • • •
• Def. Bisector • Vertical ’s• Def. Bisector . • SAS • CPCTC • Def. Alt. Int. ’s• Alt. Int. ’s are congruent • • • • • • •
Given
Prove AB || CD
Statement Reason
Line AC bis. Line BD
Proof Title:
Sketch
• A D• BC FE• B = 90- A E = 90- D
• B E• ABC DEF• BA DE• • • • • • • • •
• given• given• difference of equals• - property• ASA• CPCTC• • • • • • • •
GivenABC is a Right
BC FEA D
ProveBA DE
Statement Reason
Proof Title: Compound Bowtie #1
Sketch
• • AGE+EGB CGF+ FGD• • AGB CGD• FGD EGB• • ABGCDG• DFG BEG• • • • • •
• Given• Vertical ’s• Given• SAS • Vertical ’s• Given • Alt. Int. ’s• ASA• CPCTC • • • • •
Given
Prove
Statement Reason
CGAG
DGBG
FGEG
DGBG
CGAG
DGBG
FGEG
Proof Title:
Sketch
• AED BEC • DE CE • ADC-EDC BCD ECD • ADE BCE • ADE BCE • AD BC • ADC BCD • DC CD • ADC BCD • • • • •
• Vertical ’s • Def. iso. • Dif. Of equals • Sub. Prop. • ASA • CPCTC • Sum of Equals • Reflexive Prop. • SAS • • • • •
GivenEDC is isosceles
ProveADC BCD
Statement Reason
Proof Title:
Sketch
• AE BE • AED BEC • DE CE • ADE BCE • FDE GCE • DECE • FED GEC • FD GC• EDC ECD• ADE+EDC BCE+ ECD • ADCBCD • FGDC • •
• Given • Vert. ’s• def. iso. • SAS• CPCTC• def. iso. • alt. int. ’s• CPCTC • Def. iso. • Addition prop. Of equality • • • •
GivenAEBEEDC is isosceles
ProveFG DC
Statement Reason
Proof Title: Diagonals of a Rectangle
Sketch
• AC BD • ACD BDC • CD DC• ACD BDC • AD BC• • • • • • • • • •
• Dfn. Rectangle • Dfn. Rectangle• Reflexive• SAS• CPCTC• • • • • • • • •
Given
Rectangle ABCD
Prove AD BC
Statement Reason
Proof Title:
Sketch
• BAM CAM • ABAC • B C• BAM CAM • BM CM • BMA CMA • BMC 180 • BMA = 1/2180=90=
CMA • AM bis. Of BC • • • •
• bis. • Given • Def. iso. • ASA • CPCTC • CPCTC • straight ’s• Angle Addition • • • • • •
GivenABC w/AM bis. ABAC
ProveAM bis.
Statement Reason
Proof Title:
Sketch
• ¾=5/6.6666• AD/AB=AE/AC• A A • ADE ABC• • • • • • • • • • •
• 36&2/3=4 5= 20 • CPSTP• Reflexive • SAS • • • • • • • • • •
GivenDE || BC
ProveADE ABC
Statement Reason
Proof Title: Simple butterfly
Sketch
• AEBE • BEDAEC • CE DE • AC BD • • • • • • • • • • •
• Given • Vertical angels • Given • CPCTC • • • • • • • • • •
GivenAEBECEDE
ProveAC BD
Statement Reason
Proof Title:
Sketch
• BCA EFD • FC CF • AF CD • AF + FC DC + CF • ABC DEF • • • • • • • • • •
• Alt. Int. ’s • Reflexive • Given • Addition • ASA • • • • • • • • •
GivenAF DCFE || CBAB || DE
ProveABC DEF
Statement Reason
Proof Title:
Sketch
• BG EG • EG + GF=BG+GC • BC EF• FC FC• AF+FC=DC+CF• GFC GCF • AC=CD• ABC DEF • • • • • • •
• Given • Sum’s of =‘s• Segment addition • reflexive • Sum’s of =‘s • def. isosceles • Segment Addition • SAS• • • • • •
GivenFGC Isosceles AF DCBG EG
ProveABC DEF
Statement Reason
Proof Title: Isos. Triangle to bisector
Sketch
• BM CM • AMB = 90 = AMC• AB AC • B C• BAM CAM• BAM CAM• AM is bis. of A• • • • • • • •
• Def. bis. • Def. bis.• given• def. isos. triangle• SAS• CPCTC• • • • • • • •
GivenD ABC is isos.
AB ACAM is
Prove bis. of BC is bis.
Of A
Statement Reason
Proof Title:
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• • • • • • • •
• Def. Alt. • isos triangle• sums• sums• transitive • - property• • • • • • • •
Given ABC is isos.
AC ABAM is Alt.
Prove Alt. AM is bis. of
A
Statement Reason
Proof Title:
Sketch
• AB AC• C B• AMB=90= AMC• BAM CAM• BM CM• Alt. AM is bis. of BC• • • • • • • • •
• given • def. of isos.• def. Alt.• sums• ASA• CPCTC• • • • • • • •
Given ABC is isos.
AB ACAM is Alt.
Prove Alt. AM is bis. of
BC
Statement Reason
Proof Title: Bisectors Of An Isosceles Trapezoid
Sketch
• ACD BDC• CD DC • CEA DEB • AC BD • C D • CE DE • ACE BED • AE BE • • •
• Base ’s • Reflexive Property • Alternate Interior ’s • Definition Isosceles • Base ’s • Definition of Midpoint• SAS • • • •
GivenTrapezoid ABCD is
and isosceles E is midpoint of CD
ProveAE BE
Statement Reason
Proof Title: Pythagorean Theorem
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
•
• Given • Through a pt. there is 1 line
to a given line • Either leg is geom. Mean
bet. Hyp. And adj. seg. • Multi proportion prop. • Either leg is geom. Mean
bet. Hyp and adj. seg. • Multi. Propportion prop. • Distributive Prop. • Substitution• • •
GivenRt. ABC
Provea2+b2=c2
Statement Reason
Proof Title:
Sketch
• DAB CAB• DBA CBA• AB AB• ABD ABC• • • • • • • • • • • • •
• Given• Given • Reflexive Property• ASA• • • • • • • • • •
GivenDAB CABDBA CBA
Prove ABD ABC
Statement Reason
Proof Title: Compound Butterfly #1
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
• given • vert. ’s• given• SAS• CPCTC • sums ’s
• - prop • ASA• given• CPCTC• supp. ’s• supp. ’s• sums ’s• - prop• ASA
Given AE FE, DE JE
BEC GEHAEB FEG
Prove BEC GEH
Statement Reason
Proof Title:
Sketch
• • • • • • • • • • • • • • •
• • • • • • • • • • • • • •
Given
Prove
Statement Reason