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Flowchart Proving Other Conjectures

Flowchart Proving Other Conjectures. ABC is isosceles w/ vertex A. Given. A. Given: ABC is isosceles w/ vertex A. 1  2 Prove: 3  4. 1  2 Given. Reflexive. DBC  ECB ITC. D. 3. 4. E. 5. 6. 3&5, 4&6 form a LP (defn of LP).

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Flowchart Proving Other Conjectures

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  1. Flowchart ProvingOther Conjectures

  2. ABC is isosceles w/ vertex A. Given A • Given: ABC is isosceles w/ vertex A. 1  2 Prove: 3  4 1  2 Given Reflexive DBC  ECB ITC D 3 4 E 5 6 3&5, 4&6 form a LP (defn of LP) DBC  ECB ASA  conj 1 2 C B 5  6 CPCTC 3&5, 4&6 are supp LPC 3  4 SCAC

  3. 3&5, 4&6 form a LP & are supplementary (defn of LP & LP Conj) 3  4 Given S 2) Given: 1  2, 3  4 Prove: 1  2 Given Reflexive 5  6 SCAC 1 2  7&  8 form a LP defn of LP SPV  SQV SAA  conj 6 5 7 8 P Q 4 3 V 7  8 CPCTC  7&  8 are supp. LPC 7 & 8 are right. CSAR Defn of 

  4. C F G 7 8 5 6 1 2 4 3 B A E D 1&2, 3&4 form a LP & are supplementary (defn of LP & LP Conj) ABC is iso. w/ vertex C. Given 3) Given: ABC is isosceles w/ vertex C. 1  4, Prove: 7  8 1  4 Given Reflexive Given A  B ITC Common Segment 2  3 SCAC 5&7, 6&8 form a LP defn of LP AFE  BGD ASA  conj CPCTC 5&7, 6&8 are supp LPC 7  8 SCAC

  5. 1&3, 2&4 form a LP defn of LP 1&3, 2&4 are supp. LPC T is the midpoint of . Given Given 1  2 Given 5 & 6 are right. Defn of  Defn of midpoint 5  6 ARAC 3  4 SCAC XNT  YQT SAA  conj Z CPCTC X Y 6 5 1 3 4 2 E A Q N T 4) Given: T is the midpoint of . 1  2 Prove:

  6. KGI is isosceles. (Given) is an bisector. (Given) Reflexive Defn of Isosceles  12 Defn of bisector K 1 2 GOK  IOK SAS  conj 4 3 O CPCTC I G H 5) Given: KGI is isosceles with vertex K. is an bisector. Prove: 3 4

  7. KGI is isosceles. (Given) is an altitude. (Given) is a median. (VABC)  (defn of altitude) 3 & 4 are right. (defn of  segments) H is a midpoint. (defn of median) ARAC Reflexive Defn of midpt K GOH  IOH SAS  conj O 1 2 3 4 CPCTC I G H 6) Given: KGI is isosceles with vertex K. is an altitude. Prove: 1 2

  8. E C N B P D A Reflexive 7) Given: B & N are supplementary. Prove: B & N are right. Given Given Given ACB  DEN (ITC) Common Segment ABC  DNE SAA  conj B & N are supplementary. Given CPCTC B & N are right. CSAR

  9. BAD  EAC Given 1  2 Given CAD is isosceles, (CITC) BAD  EAC ASA  conj Reflexive CPCTC Common Segment A 1 2 B E C D 8) Given: BAD  EAC 1  2 Prove:

  10. 1  2 Given 3  3 Reflexive T  E Given BAE  MAT Common Angle Given B ABE  AMT SAA  conj T E CPCTC 3 1 2 A M 9) Given: T  E 1  2 Prove:

  11. A C B E D ABD & CBE are right. Given 10) Given: ABD and CBE are right. Prove: D  E DBE  DBE Reflexive ABD  CBE ARAC Given ABE  CBD Common Angle Given ABE  CBD SAS  conj D  E CPCTC

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