Which of the following statements must be true based on the diagram below? (Diagram is not to scale.) F O BF is a segment bisector. O B is the vertex of a pair of congruent angles in the diagram. O F is the vertex of a pair of congruent angles in the diagram. O Bis the midpoint of a segment in the diagram. O Fis the midpoint of a segment in the diagram. O None of the above
Which of the following statements must be true based on the diagram below? (Diagram is not to scale.) F O BF is a segment bisector. O B is the vertex of a pair of congruent angles in the diagram. O F is the vertex of a pair of congruent angles in the diagram. O Bis the midpoint of a segment in the diagram. O Fis the midpoint of a segment in the diagram. O None of the above
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: Analyzing Geometric Diagrams
**Instructions:**
Observe the diagram provided below and determine which of the following statements must be true based on the diagram.
*(Note: The diagram is not to scale.)*
**Diagram:**
A triangle is depicted with vertices labeled \( D, B, \) and \( C \). A line segment \( DF \) extends from vertex \( D \) and intersects \( BC \) at point \( F \). The segments \( DF \) and \( FC \) are marked with congruency ticks, indicating they are of equal length.
**Statements to Examine:**
1. \( BF \) is a segment bisector.
2. \( B \) is the vertex of a pair of congruent angles in the diagram.
3. \( F \) is the vertex of a pair of congruent angles in the diagram.
4. \( B \) is the midpoint of a segment in the diagram.
5. \( F \) is the midpoint of a segment in the diagram.
6. None of the above.
**Explanation of the Diagram:**
The diagram shows a triangle \( DBC \) with an additional point \( F \) lying on segment \( BC \). Two segments, \( DF \) and \( FC \), are shown as equal (indicated by the congruency markings on these segments).
**Evaluation of Statements:**
From the given information in the diagram:
- The congruency marks explicitly indicate that \( DF = FC \).
- To determine if \( F \) is the midpoint of segment \( BC \), we consider that for \( F \) to be the midpoint, it must equally divide \( BC \). Given \( DF = FC \), it appears \( F \) is indeed the midpoint.
Therefore, the most accurate statement is:
- \( F \) is the midpoint of a segment in the diagram.
**Conclusion:**
The correct answer is:
\[ \boxed{F \text{ is the midpoint of a segment in the diagram.}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a0b07f5-f33b-4824-9179-7b732f37d42c%2F835f276b-a40c-42d9-849d-6bcb12602c13%2F5vgixdw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question: Analyzing Geometric Diagrams
**Instructions:**
Observe the diagram provided below and determine which of the following statements must be true based on the diagram.
*(Note: The diagram is not to scale.)*
**Diagram:**
A triangle is depicted with vertices labeled \( D, B, \) and \( C \). A line segment \( DF \) extends from vertex \( D \) and intersects \( BC \) at point \( F \). The segments \( DF \) and \( FC \) are marked with congruency ticks, indicating they are of equal length.
**Statements to Examine:**
1. \( BF \) is a segment bisector.
2. \( B \) is the vertex of a pair of congruent angles in the diagram.
3. \( F \) is the vertex of a pair of congruent angles in the diagram.
4. \( B \) is the midpoint of a segment in the diagram.
5. \( F \) is the midpoint of a segment in the diagram.
6. None of the above.
**Explanation of the Diagram:**
The diagram shows a triangle \( DBC \) with an additional point \( F \) lying on segment \( BC \). Two segments, \( DF \) and \( FC \), are shown as equal (indicated by the congruency markings on these segments).
**Evaluation of Statements:**
From the given information in the diagram:
- The congruency marks explicitly indicate that \( DF = FC \).
- To determine if \( F \) is the midpoint of segment \( BC \), we consider that for \( F \) to be the midpoint, it must equally divide \( BC \). Given \( DF = FC \), it appears \( F \) is indeed the midpoint.
Therefore, the most accurate statement is:
- \( F \) is the midpoint of a segment in the diagram.
**Conclusion:**
The correct answer is:
\[ \boxed{F \text{ is the midpoint of a segment in the diagram.}} \]
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