# 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.

Answered: Image /qna-images/answer/3f9604c0-0625-4e41-b2a8-8d2470787af2.jpg

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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Question

# 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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