Using Two Pairs of Congruent Triangles in a Proof.

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Presentation transcript:

Using Two Pairs of Congruent Triangles in a Proof

D C B A E Prove: CE  DE 1.AEB, AC  AD, 1. Given BC  BD 1) 2. AB  AB2. Reflexive 3.  ACB   ADB3. SSS  SSS 4.  CAE   DAE4. CPCTC 5. AE  AE5. Reflexive 6.  ACE   ADE6. SAS  SAS 7. CE  DE7. CPCTC

N I V E K Prove: NE bisects KV 1.NK  NV, 1. Given IK  IV 2) 2. IN  IN 2. Reflexive 3.  KIN   VIN 3. SSS  SSS 4. <KNE  <VNE4. CPCTC 5. NE  NE5. Reflexive 6.  KEN   VEN 6. SAS  SAS 7.KE  VE7. CPCTC 8.NE bisects KV8. A segment is bisected if it is cut in half. Plan:

C AB E D F G 1.AD  CB, DC  BA 1. Given EF bisects BD Prove: FG  EG 3) 5. DG  BG 5. A bisector cuts in half 2.BD  BD2. Reflexive 3.  ABD   CDB3. SSS  SSS 4.  CDB   ABD 4. CPCTC 6.  DGE   BGF6. Vertical Angles are congruent 7.  DGE   BGF7. ASA  ASA 8. FG  EG8. CPCTC

Q A D C B P 21 Prove: QB  QD 1.  1   2, AP  CP 1. Given PQ, PAB, PCD, AQD, CQB 2.PQ  PQ 2. Reflexive 3.  PAQ   PCQ 3. SAS  SAS 4.QA  QC 4. CPCTC  QAP   QCP 5.  BAQ is suppl to  QAP 5. Linear pairs are  DCQ is suppl. to  PCQ supplements. 6.  BAQ   DCQ 6. 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. CPCTC

Homework: Pairs of Congruent Triangles D E C G A FB Prove: GE  GF 1.AC and BD bisect1. Given each other at G, EGF 1) 2. AG  CG, BG  DG2. A bisector cuts in half 3.  AGB   CGD3. Vertical  ’s are  4.  AGB   CGD4. SAS  SAS 5.  A   C5. CPCTC 6.  AGF   CGE6. Vertical  ’s are  7.  AGB   CGD 7. ASA  ASA 8. GE  GF8. CPCTC

2) B C A D 1E 2 Prove:  1   2 1.AC  AD, BC  BD1. Given AB intersects CD at E 2.AB  AB2. Reflexive 3.  ABC   ABD3. SSS  SSS 4.  CAB   DAB4. CPCTC 5.  ACE   ADE5. If 2 sides of a  are , then opposite  ’s are  6.  ADE   ACE6. ASA  ASA 7.  1   22. CPCTC

3) T PQ R S 1.RP  RQ, SP  SQ1. Given Prove: RT bisects PQ 2. RS  RS2. Reflexive 3.  RPS   RQS3. SSS  SSS 4.  PRS   QRS4. CPCTC 5.  RPT   RQT5. If 2 sides of a  are , then opposite  ’s are  6.  RPT   RQT6. ASA  ASA 7. PT  QT7. CPCTC 8.RT bisects PQ8. A segment is bisected if its cut in half