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Using Two Pairs of Congruent Triangles in a Proof

Using Two Pairs of Congruent Triangles in a Proof. AEB, AC  AD, 1. Given BC  BD. 1). 2. AB  AB 2. Reflexive. C. 3. ACB  ADB 3. SSS  SSS. 4. CAE  DAE 4. CPCTC. E. B. A. 5. AE  AE 5. Reflexive. 6. ACE  ADE 6. SAS  SAS. D. 7. CE  DE 7. CPCTC.

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Using Two Pairs of Congruent Triangles in a Proof

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  1. Using Two Pairs of Congruent Triangles in a Proof

  2. AEB, AC  AD, 1. Given • BC  BD 1) 2. AB  AB 2. Reflexive C 3.ACB  ADB 3. SSS  SSS 4. CAE  DAE 4. CPCTC E B A 5. AE  AE 5. Reflexive 6. ACE  ADE 6. SAS  SAS D 7.CE  DE 7. CPCTC Prove: CE  DE

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

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

  5. 1  2, AP  CP 1. Given • PQ, PAB, PCD, • AQD, CQB B D • PQ  PQ 2. Reflexive • PAQ  PCQ 3. SAS  SAS Q • QA  QC 4. CPCTC • QAP  QCP A C 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  1 2 P 7. BQA  DQC 7. Vertical <‘s are  Prove: QB  QD 8. PAQ  PCQ 8. ASA  ASA 9. QB  QD 9. CPCTC

  6. Homework: Pairs of Congruent Triangles • AC and BD bisect 1. Given • each other at G, • EGF 1) D E C 2. AG  CG, BG  DG 2. A bisector cuts in half 3. AGB  CGD 3. Vertical ’s are  G 4. AGB  CGD 4. SAS  SAS 5. A  C 5. CPCTC 6.AGF  CGE 6. Vertical ’s are  A 7. AGB  CGD 7. ASA  ASA F B 8. GE  GF 8. CPCTC Prove: GE  GF

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

  8. 3) • RP  RQ, SP  SQ 1. Given R 2. RS  RS 2. Reflexive 3. RPS  RQS 3. SSS  SSS 4. PRS  QRS 4. CPCTC 5. RPT  RQT 5. If 2 sides of a  are , then opposite ’s are  6. RPT  RQT 6. ASA  ASA 7. PT  QT 7. CPCTC S • RT bisects PQ 8. A segment is bisected if its cut in half P Q T Prove: RT bisects PQ

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