Elementary Geometry For College Students, 7e
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ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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### Geometry Proofs: Identifying Reasons for Vertical Angles
In geometry, constructing a proof often involves identifying the proper reasons supporting given statements. Below is an example that illustrates this concept:
**Problem:**
**Select the proper reason if this statement is provided as a fact at the beginning of a proof.**
**Statement**
∠7 and ∠8 are vertical angles
**Reason**
[ ? ]
Options:
- A. Truth
- B. Given
- C. Postulate
---
**Explanation:**
When developing a proof in geometry, identifying why a statement is true is crucial. In the problem above, the statement "∠7 and ∠8 are vertical angles" needs a corresponding reason.
Typically, reasons can be categorized as follows:
- **Given:** The statement is directly provided within the problem.
- **Postulate:** The statement is based on an accepted postulate, which is a fundamental truth used as a basis for reasoning.
- **Truth:** This generally refers to a fact derived from logical reasoning or definitions, although "Truth" is not a standard option in most formal proof tables and might be considered an invalid choice here.
For the statement "∠7 and ∠8 are vertical angles," the appropriate reason would likely be **B. Given** if it is directly provided within the problem context.
Vertical angles are typically defined as the angles opposite each other when two lines intersect. They are always equal to each other, forming key components in geometric proofs.
---
Understanding the foundations of geometric proofs is essential for solving more complex problems. Remember, the proper categorization of statements and reasons serves as the backbone of logical reasoning in mathematics.
---](https://content.bartleby.com/qna-images/question/a4f77774-5e37-4187-b554-2e9655af3f68/1c2d3533-9257-4d42-9bed-36c2b71972df/1eb9i1n_processed.jpeg)
Transcribed Image Text:---
### Geometry Proofs: Identifying Reasons for Vertical Angles
In geometry, constructing a proof often involves identifying the proper reasons supporting given statements. Below is an example that illustrates this concept:
**Problem:**
**Select the proper reason if this statement is provided as a fact at the beginning of a proof.**
**Statement**
∠7 and ∠8 are vertical angles
**Reason**
[ ? ]
Options:
- A. Truth
- B. Given
- C. Postulate
---
**Explanation:**
When developing a proof in geometry, identifying why a statement is true is crucial. In the problem above, the statement "∠7 and ∠8 are vertical angles" needs a corresponding reason.
Typically, reasons can be categorized as follows:
- **Given:** The statement is directly provided within the problem.
- **Postulate:** The statement is based on an accepted postulate, which is a fundamental truth used as a basis for reasoning.
- **Truth:** This generally refers to a fact derived from logical reasoning or definitions, although "Truth" is not a standard option in most formal proof tables and might be considered an invalid choice here.
For the statement "∠7 and ∠8 are vertical angles," the appropriate reason would likely be **B. Given** if it is directly provided within the problem context.
Vertical angles are typically defined as the angles opposite each other when two lines intersect. They are always equal to each other, forming key components in geometric proofs.
---
Understanding the foundations of geometric proofs is essential for solving more complex problems. Remember, the proper categorization of statements and reasons serves as the backbone of logical reasoning in mathematics.
---
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