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# Educational Content: Geometry Problem on Medians of a Triangle ## Problem Statement: **#18: In the diagram of triangle ABC below, medians AD and BE intersect at point F. If AF = 6, what is the length of FD?** *Reference Code: G.CO.C.10* ## Diagram Description: The provided diagram is a triangle labeled **ABC**. Two of the medians, **AD** and **BE**, are drawn from vertices **A** and **B** respectively to the midpoints of the opposite sides. These medians intersect at point **F**, the centroid of the triangle. The length **AF** is marked as 6. The task is to find the length of **FD**. ### Multiple Choice Options: - **A. 6** - **B. 2** - **C. 3** - **D. 9** ### Detailed Diagram Description: In this triangle: - Vertex **A** is at the top. - Vertex **B** is at the bottom left. - Vertex **C** is at the bottom right. - **D** is the midpoint of side **BC**. - **E** is the midpoint of side **AC**. - **F** is the centroid where medians **AD** and **BE** intersect. ### Important Concept: One significant property of the centroid (point **F**) in a triangle is that it divides each median into a ratio of 2:1. That means, **AF** is twice the length of **FD**. ### Solution: Since **AF** is given as 6, **FD** can be calculated as follows: \[ AF = 2 \times FD \] \[ 6 = 2 \times FD \] \[ FD = \frac{6}{2} \] \[ FD = 3 \] ### Correct Answer: **C. 3**

# Educational Content: Geometry Problem on Medians of a Triangle ## Problem Statement: **#18: In the diagram of triangle ABC below, medians AD and BE intersect at point F. If AF = 6, what is the length of FD?** *Reference Code: G.CO.C.10* ## Diagram Description: The provided diagram is a triangle labeled **ABC**. Two of the medians, **AD** and **BE**, are drawn from vertices **A** and **B** respectively to the midpoints of the opposite sides. These medians intersect at point **F**, the centroid of the triangle. The length **AF** is marked as 6. The task is to find the length of **FD**. ### Multiple Choice Options: - **A. 6** - **B. 2** - **C. 3** - **D. 9** ### Detailed Diagram Description: In this triangle: - Vertex **A** is at the top. - Vertex **B** is at the bottom left. - Vertex **C** is at the bottom right. - **D** is the midpoint of side **BC**. - **E** is the midpoint of side **AC**. - **F** is the centroid where medians **AD** and **BE** intersect. ### Important Concept: One significant property of the centroid (point **F**) in a triangle is that it divides each median into a ratio of 2:1. That means, **AF** is twice the length of **FD**. ### Solution: Since **AF** is given as 6, **FD** can be calculated as follows: \[ AF = 2 \times FD \] \[ 6 = 2 \times FD \] \[ FD = \frac{6}{2} \] \[ FD = 3 \] ### Correct Answer: **C. 3**

Elementary Geometry For College Students, 7e
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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# Educational Content: Geometry Problem on Medians of a Triangle ## Problem Statement: **#18: In the diagram of triangle ABC below, medians AD and BE intersect at point F. If AF = 6, what is the length of FD?** *Reference Code: G.CO.C.10* ## Diagram Description: The provided diagram is a triangle labeled **ABC**. Two of the medians, **AD** and **BE**, are drawn from vertices **A** and **B** respectively to the midpoints of the opposite sides. These medians intersect at point **F**, the centroid of the triangle. The length **AF** is marked as 6. The task is to find the length of **FD**. ### Multiple Choice Options: - **A. 6** - **B. 2** - **C. 3** - **D. 9** ### Detailed Diagram Description: In this triangle: - Vertex **A** is at the top. - Vertex **B** is at the bottom left. - Vertex **C** is at the bottom right. - **D** is the midpoint of side **BC**. - **E** is the midpoint of side **AC**. - **F** is the centroid where medians **AD** and **BE** intersect. ### Important Concept: One significant property of the centroid (point **F**) in a triangle is that it divides each median into a ratio of 2:1. That means, **AF** is twice the length of **FD**. ### Solution: Since **AF** is given as 6, **FD** can be calculated as follows: \[ AF = 2 \times FD \] \[ 6 = 2 \times FD \] \[ FD = \frac{6}{2} \] \[ FD = 3 \] ### Correct Answer: **C. 3**
Transcribed Image Text:# Educational Content: Geometry Problem on Medians of a Triangle ## Problem Statement: **#18: In the diagram of triangle ABC below, medians AD and BE intersect at point F. If AF = 6, what is the length of FD?** *Reference Code: G.CO.C.10* ## Diagram Description: The provided diagram is a triangle labeled **ABC**. Two of the medians, **AD** and **BE**, are drawn from vertices **A** and **B** respectively to the midpoints of the opposite sides. These medians intersect at point **F**, the centroid of the triangle. The length **AF** is marked as 6. The task is to find the length of **FD**. ### Multiple Choice Options: - **A. 6** - **B. 2** - **C. 3** - **D. 9** ### Detailed Diagram Description: In this triangle: - Vertex **A** is at the top. - Vertex **B** is at the bottom left. - Vertex **C** is at the bottom right. - **D** is the midpoint of side **BC**. - **E** is the midpoint of side **AC**. - **F** is the centroid where medians **AD** and **BE** intersect. ### Important Concept: One significant property of the centroid (point **F**) in a triangle is that it divides each median into a ratio of 2:1. That means, **AF** is twice the length of **FD**. ### Solution: Since **AF** is given as 6, **FD** can be calculated as follows: \[ AF = 2 \times FD \] \[ 6 = 2 \times FD \] \[ FD = \frac{6}{2} \] \[ FD = 3 \] ### Correct Answer: **C. 3**
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