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
Related questions
Question
I answer this ples
![**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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f38e2ce-2517-4530-8b0d-a9b44a7c4ae2%2Fccaef6ed-5df5-4d12-bd68-cbcd598a0df7%2Fcuyes8_processed.jpeg&w=3840&q=75)
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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