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
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8e190d3-15de-4cd5-babb-70573add2167%2F3f9604c0-0625-4e41-b2a8-8d2470787af2%2F8dmobj_processed.jpeg&w=3840&q=75)
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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