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Date: Name: Given: BA BC and DA = EC Prove: BD = BE Statements O PA BC 2 BA= BC and DA= EC 3 BD + DA = BA 4 BE +EC = BC 5 BD + DA= BC BD + DA=BE+EC BD+ DA =BE+DA 8 BD = BE BD BE D (8) 6 A Period: B Reasons Ⓒ Jiken 2 Det of congruence (3) 4 6 Substitution substitution substitution C

Date: Name: Given: BA BC and DA = EC Prove: BD = BE Statements O PA BC 2 BA= BC and DA= EC 3 BD + DA = BA 4 BE +EC = BC 5 BD + DA= BC BD + DA=BE+EC BD+ DA =BE+DA 8 BD = BE BD BE D (8) 6 A Period: B Reasons Ⓒ Jiken 2 Det of congruence (3) 4 6 Substitution substitution substitution C

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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# Geometry Proof Worksheet ### Given Information: - \( \overline{BA} \cong \overline{BC} \) - \( \overline{DA} \cong \overline{EC} \) ### To Prove: - \( \overline{BD} \cong \overline{BE} \) ### Diagram: A triangle diagram is provided with points A, B, C, D, and E. ### Proof: The following table outlines the step-by-step proof provided. | Statements | Reasons | |----------------------------|--------------------------| | 1. \( \overline{BA} \cong \overline{BC} \) | Given | | 2. \( \overline{BA} = \overline{BC} \) and \( \overline{DA} = \overline{EC} \) | Definition of Congruence | | 3. \( \overline{BD} + \overline{DA} = \overline{BA} \) | | | 4. \( \overline{BE} + \overline{EC} = \overline{BC} \) | | | 5. \( \overline{BD} + \overline{DA} = \overline{BE} + \overline{EC} \) | Substitution | | 6. \( \overline{BD} + \overline{DA} = \overline{BE} + \overline{DA} \) | Substitution | | 7. \( \overline{BD} + \overline{DA} = \overline{BE} + \overline{DA} \) | Substitution | | 8. \( \overline{BD} \cong \overline{BE} \) | | This worksheet illustrates the process of proving segment congruence using given information and congruence properties. The logic flow demonstrates substitution and properties of equality and congruence in geometric proofs.
Transcribed Image Text:# Geometry Proof Worksheet ### Given Information: - \( \overline{BA} \cong \overline{BC} \) - \( \overline{DA} \cong \overline{EC} \) ### To Prove: - \( \overline{BD} \cong \overline{BE} \) ### Diagram: A triangle diagram is provided with points A, B, C, D, and E. ### Proof: The following table outlines the step-by-step proof provided. | Statements | Reasons | |----------------------------|--------------------------| | 1. \( \overline{BA} \cong \overline{BC} \) | Given | | 2. \( \overline{BA} = \overline{BC} \) and \( \overline{DA} = \overline{EC} \) | Definition of Congruence | | 3. \( \overline{BD} + \overline{DA} = \overline{BA} \) | | | 4. \( \overline{BE} + \overline{EC} = \overline{BC} \) | | | 5. \( \overline{BD} + \overline{DA} = \overline{BE} + \overline{EC} \) | Substitution | | 6. \( \overline{BD} + \overline{DA} = \overline{BE} + \overline{DA} \) | Substitution | | 7. \( \overline{BD} + \overline{DA} = \overline{BE} + \overline{DA} \) | Substitution | | 8. \( \overline{BD} \cong \overline{BE} \) | | This worksheet illustrates the process of proving segment congruence using given information and congruence properties. The logic flow demonstrates substitution and properties of equality and congruence in geometric proofs.
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