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Given: BA = BC <ABD = <CBE Prove: BE = BD (by proving ∆ABE = ∆CBD)

B. Given: BA = BC <ABD = <CBE Prove: BE = BD (by proving ∆ABE = ∆CBD). <1. <2. <3. <4. <5. <6. <7. A. C. E. D. Statement Reason BA = BC given <ABD = <CBE given. B. Given: BA = BC <ABD = <CBE Prove: BE = BD (by proving ∆ABE = ∆CBD). <1. <2. <3. <4. <5. <6. <7.

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Given: BA = BC <ABD = <CBE Prove: BE = BD (by proving ∆ABE = ∆CBD)

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  1. B Given: BA = BC <ABD = <CBE Prove: BE = BD (by proving ∆ABE = ∆CBD) <1 <2 <3 <4 <5 <6 <7 A C E D Statement Reason BA = BC given <ABD = <CBE given

  2. B Given: BA = BC <ABD = <CBE Prove: BE = BD (by proving ∆ABE = ∆CBD) <1 <2 <3 <4 <5 <6 <7 A C E D Statement Reason BA = BC given <ABD = <CBE given <ABD = <1 + <2 angle addition postulate <CBE = <2 + <3 angle addition postulate <1 + <2 = <2 + <3 substitution <1 = <3 subtraction <A = <C base angles theorem ∆ABE = ∆CBD ASA BE = BD CPCTC

  3. B Given: BA = BC <ABD = <CBE Prove: BE = BD (by proving ∆ABD = ∆CBE) <1 <2 <3 <4 <5 <6 <7 A C E D Statement Reason BA = BC given <ABD = <CBE given

  4. B Given: BA = BC <ABD = <CBE Prove: BE = BD (by proving ∆ABD = ∆CBE) <1 <2 <3 <4 <5 <6 <7 A C E D Statement Reason BA = BC given <ABD = <CBE given <A = <C base angles theorem ∆ABD = ∆CBE ASA BE = BD CPCTC

  5. B Given: AC bisects <A AC bisects <C Prove: ∆ABC = ∆ADC <1 <3 A C <2 X <4 D Statement Reason AC bisects <A given AC bisects <C given

  6. B Given: AC bisects <A AC bisects <C Prove: ∆ABC = ∆ADC <1 <3 A C <2 X <4 D Statement Reason AC bisects <A given AC bisects <C given <1 = <2 definition of angle bisector <3 = <4 definition of angle bisector AC = AC reflexive property ∆ABC = ∆ADC ASA

  7. B Given: AC bisects <A AC bisects <C Prove: ∆ABX = ∆ADX hint: prove ∆ABC = ∆ADC <1 <3 A C <2 X <4 D Statement Reason AC bisects <A given AC bisects <C given

  8. B Given: AC bisects <A AC bisects <C Prove: ∆ABX = ∆ADX <1 <3 A C <2 X <4 D Statement Reason AC bisects <A given AC bisects <C given <1 = <2 definition of angle bisector <3 = <4 definition of angle bisector AC = AC reflexive property ∆ABC = ∆ADC ASA AB = AD CPCTC AX = AX reflexive property ∆ABX = ∆ADX SAS

  9. B Given: AC bisects <A AC bisects <C Prove: <XBC = <XDC <1 <3 A C <2 X <4 D Statement Reason AC bisects <A given AC bisects <C given

  10. B Given: AC bisects <A AC bisects <C Prove: <XBC = <XDC <1 <3 A C <2 X <4 D Statement Reason AC bisects <A given AC bisects <C given <1 = <2 definition of angle bisector <3 = <4 definition of angle bisector AC = AC reflexive property ∆ABC = ∆ADC ASA BC = DC CPCTC <XBC = <XDC base angles theorem

  11. B Given: AC bisects <A AC bisects <C Prove: BX = DX <1 <3 A C <2 X <4 D Statement Reason AC bisects <A given AC bisects <C given

  12. B Given: AC bisects <A AC bisects <C Prove: BX = DX <1 <3 A C <2 X <4 D Statement Reason AC bisects <A given AC bisects <C given <1 = <2 definition of angle bisector <3 = <4 definition of angle bisector AC = AC reflexive property ∆ABC = ∆ADC ASA AB = AD CPCTC AX = AX reflexive property ∆ABX = ∆ADX SAS BX = DX CPCTC

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