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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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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&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
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
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:
KGI is isosceles. (Given) is an bisector. (Given) Reflexive Defn of Isosceles 12 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
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
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
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:
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:
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
