Transcript
Using Two Pairs of Congruent Triangles in a ProofDCBAEProve:CE ? DEAEB, AC ? AD, 1.GivenBC ? BD1)2.AB ? AB 2.Reflexive3.?ACB ? ?ADB 3.SSS ? SSS 4.?CAE ? ?DAE 4.CPCTC5.AE ? AE 5.Reflexive6.?ACE ? ?ADE 6.SAS ? SAS 7. CE ? DE 7.CPCTCNIVEKProve:NE bisects KVNK ? NV, 1.GivenIK ? IV2)2.IN ? IN 2.Reflexive3.?KIN ? ?VIN 3.SSS ? SSS4.<KNE ? <VNE 4.CPCTC5.NE? NE 5.Reflexive6.?KEN ? ?VEN 6.SAS ? SASKE ? VE 7.CPCTCNE bisects KV 8.A segment is bisected if it is cut in half.Plan:CABEDFGAD ? CB, DC ? BA 1.Given EF bisects BDProve:FG ? EG3)5.DG ? BG 5.A bisector cuts in halfBD ? BD 2.Reflexive?ABD ? ?CDB 3.SSS ? SSS4.?CDB ? ?ABD4.CPCTC6. ?DGE? ?BGF 6.Vertical Angles are congruent 7.?DGE ? ?BGF 7.ASA ? ASA8. FG ? EG 8.CPCTCQADCBP21Prove:QB ? QD?1 ? ?2, AP ? CP 1.Given PQ, PAB, PCD, AQD, CQBPQ? PQ 2. Reflexive?PAQ ? ?PCQ 3.SAS ? SASQA? QC 4.CPCTC ?QAP ? ?QCP5. ?BAQ is suppl to ?QAP5.Linear pairs are?DCQ is suppl. to ?PCQsupplements.6. ?BAQ ? ?DCQ6.It 2 <‘s are ?, then their suppelments are ?7. ?BQA ? ?DQC 7.Vertical <‘s are ?8.?PAQ ? ?PCQ 8.ASA ? ASA 9.QB ? QD 9.CPCTCHomework:Pairs of Congruent TrianglesDECGAFBProve:GE ? GFAC and BD bisect 1.Given each other at G, EGF1)2.AG ? CG, BG ? DG 2.A bisector cuts in half3.?AGB ? ?CGD 3.Vertical ?’s are?4.?AGB ? ?CGD 4.SAS ? SAS5.?A ? ?C 5.CPCTC6. ?AGF ? ?CGE 6.Vertical ?’s are?7. ?AGB ? ?CGD 7.ASA ? ASA 8.GE ? GF 8.CPCTC2)BCAD1E2Prove:?1? ?2AC ? AD, BC ? BD 1. GivenAB intersects CDat EAB ? AB 2.Reflexive?ABC ? ?ABD 3.SSS ? SSS4.?CAB ? ?DAB 4.CPCTC5.?ACE ? ?ADE 5.If 2 sides of a ? are ?, then opposite ?’s are ?6.?ADE ? ?ACE 6.ASA ? ASA7.?1 ? ?2 2.CPCTC3)TPQRSRP ? RQ, SP ? SQ 1. GivenProve:RT bisects PQ2. RS ? RS 2.Reflexive3.?RPS ? ?RQS 3.SSS ? SSS4.?PRS ? ?QRS 4.CPCTC5.?RPT ? ?RQT 5.If 2 sides of a ? are ?, then opposite ?’s are ?6. ?RPT ? ?RQT 6.ASA ? ASA 7.PT ? QT 7.CPCTCRT bisects PQ 8.A segment is bisected if its cut in half
