Write a two-column proof to show the following: A C B D Given: AB= CD Prove: CD = AB

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
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**Title: Geometric Proofs: Two-Column Proof Example**

**Objective:**
Write a two-column proof to show the following: Given: \( AB = CD \)  
Prove: \( CD = AB \)

### Diagram:
The diagram shows two line segments, \( AB \) and \( CD \), which are parallel and equal in length.

```
A -------------------- B
C -------------------- D
```

### Proof:
Given: \( AB = CD \)  
Prove: \( CD = AB \)

| **Statements**             | **Reasons**                  |
|----------------------------|------------------------------|
| 1. \( AB = CD \)             | 1. Given                      |
| 2. \( CD = AB \)             | 2. Symmetric Property of Equality |

### Notes:
- **Symmetric Property of Equality:** This property states that if one quantity equals a second quantity, then the second quantity equals the first.

**Instructions for Students:**
- Use the paperclip button below to attach files if needed.
- Student can enter max 2000 characters.

**Student Input Section:**
[Text input area for student response]

By understanding the symmetric property and how to apply it, students gain a solid foundation for constructing basic geometric proofs on their own.

---

**References:**
- Geometry Textbook, Chapter on Proofs
- Online Geometry Tools and Resources
Transcribed Image Text:**Title: Geometric Proofs: Two-Column Proof Example** **Objective:** Write a two-column proof to show the following: Given: \( AB = CD \) Prove: \( CD = AB \) ### Diagram: The diagram shows two line segments, \( AB \) and \( CD \), which are parallel and equal in length. ``` A -------------------- B C -------------------- D ``` ### Proof: Given: \( AB = CD \) Prove: \( CD = AB \) | **Statements** | **Reasons** | |----------------------------|------------------------------| | 1. \( AB = CD \) | 1. Given | | 2. \( CD = AB \) | 2. Symmetric Property of Equality | ### Notes: - **Symmetric Property of Equality:** This property states that if one quantity equals a second quantity, then the second quantity equals the first. **Instructions for Students:** - Use the paperclip button below to attach files if needed. - Student can enter max 2000 characters. **Student Input Section:** [Text input area for student response] By understanding the symmetric property and how to apply it, students gain a solid foundation for constructing basic geometric proofs on their own. --- **References:** - Geometry Textbook, Chapter on Proofs - Online Geometry Tools and Resources
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