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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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Triangle Congruence and Similarity Proofs Augustus Vitug Melissa Moize
Sketch AB AC BD DC AD AD BAD CAD Proof Title: Statement Reason • Given • Given • Reflexive property • SSS • Given AB AC BD DC Prove BAD CAD
Sketch ABC DCB CB BC DBC ACB ABC DCB CA DB AB CD Proof Title: Statement Reason • Alt. Int. ’s • reflexive • Alt. Int. ’s • ASA • CPCTC • CPCTC • 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 Proof Title: Parallelogram Diagonals Bisect Each Other Statement Reason • Alt. Int. ’s • Reflexive property • Alt. Int. ’s • ASA • CPCTC • Alt. Int. ’s • ASA • CPCTC • CPCTC Given ABCD Prove AEDE BECE
Sketch ABC DCB CB BC ACB DBC ABC DCB A D ABC + DBC DCB +ACB Proof Title: Statement Reason • Alt. Int. ’s • reflexive • Alt. Int. ’s • ASA • CPCTC • 2nd Postulate • 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 Proof Title: Compound Polygon #1 Statement Reason • 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 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 Proof Title: Compound # 2 Statement Reason • Given • Def. isos • Reflexive • SAS • Sums of Equals • Subtraction property • def. isos. 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 Proof Title: ? Statement Reason • Given • Given • Def. of Midpoint • SAS • CPCTC • CPCTC • Def. of Midpoint • SAS • CPCTC 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 Proof Title: Simple Bowtie Statement Reason • Def. Bisector • Vertical ’s • Def. Bisector . • SAS • CPCTC • Def. Alt. Int. ’s • Alt. Int. ’s are congruent 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 Proof Title: Statement Reason • given • given • difference of equals • - property • ASA • CPCTC • Given ABC is a Right BC FE A D Prove BA DE
Sketch AGE+EGB CGF+ FGD AGB CGD FGD EGB ABGCDG DFG BEG Proof Title: Compound Bowtie #1 Statement Reason • Given • Vertical ’s • Given • SAS • Vertical ’s • Given • Alt. Int. ’s • ASA • CPCTC • Given Prove
Sketch AED BEC DE CE ADC-EDC BCD ECD ADE BCE ADE BCE AD BC ADC BCD DC CD ADC BCD Proof Title: Statement Reason • Vertical ’s • Def. iso. • Dif. Of equals • Sub. Prop. • ASA • CPCTC • Sum of Equals • Reflexive Prop. • SAS • 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 Proof Title: Statement Reason • Given • Vert. ’s • def. iso. • SAS • CPCTC • def. iso. • alt. int. ’s • CPCTC • Def. iso. • Addition prop. Of equality • Given AEBE EDC is isosceles Prove FG DC
Sketch AC BD ACD BDC CD DC ACD BDC AD BC Proof Title: Diagonals of a Rectangle Statement Reason • Dfn. Rectangle • Dfn. Rectangle • Reflexive • SAS • CPCTC • 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 Proof Title: Statement Reason • bis. • Given • Def. iso. • ASA • CPCTC • CPCTC • straight ’s • Angle Addition Given ABC w/ AM bis. ABAC Prove AM bis.
Sketch ¾=5/6.6666 AD/AB=AE/AC A A ADE ABC Proof Title: Statement Reason • 36&2/3=4 5= 20 • CPSTP • Reflexive • SAS Given DE || BC Prove ADE ABC
Sketch AEBE BEDAEC CE DE AC BD Proof Title: Simple butterfly Statement Reason • Given • Vertical angels • Given • CPCTC Given AEBE CEDE Prove AC BD
Sketch BCA EFD FC CF AF CD AF + FC DC + CF ABC DEF Proof Title: Statement Reason • Alt. Int. ’s • Reflexive • Given • Addition • ASA • 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 Proof Title: Statement Reason • Given • Sum’s of =‘s • Segment addition • reflexive • Sum’s of =‘s • def. isosceles • Segment Addition • SAS • 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 Proof Title: Isos. Triangle to bisector Statement Reason • Def. bis. • Def. bis. • given • def. isos. triangle • SAS • CPCTC • • Given • ABC is isos. 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 Proof Title: Statement Reason • Def. Alt. • isos triangle • sums • sums • transitive • - property • Given ABC is isos. AC AB AM is Alt. Prove Alt. AM is bis. of A