Given the diagram below, if H is the centroid of ABCD, BG=86, CD=34, EH=15, and CF=39, find each measure. Round answers to the nearest tenth when needed. В E G F D GD= HG= BH= CH= HF=

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
icon
Related questions
icon
Concept explainers
Topic Video
Question
**Text:**

Given the diagram below, if \( H \) is the centroid of \( \triangle BCD \), \( BG = 86 \), \( CD = 34 \), \( EH = 15 \), and \( CF = 39 \), find each measure. Round answers to the nearest tenth when needed.

**Diagram Explanation:**

The diagram depicts triangle \( \triangle BCD \) with centroid \( H \). The centroid is the point where the medians of the triangle intersect. Medians are line segments drawn from a vertex to the midpoint of the opposite side. Points \( E \), \( F \), and \( G \) represent midpoints of sides \( BC \), \( BD \), and \( CD \) respectively.

The following line segments are given or need to be determined:

- \( GD \) = ________
- \( HG \) = ________
- \( BH \) = ________
- \( CH \) = ________
- \( HF \) = ________
- \( ED \) = ________

**Known Values:**

- \( BG = 86 \)
- \( CD = 34 \)
- \( EH = 15 \)
- \( CF = 39 \)

**Concepts to Use:**

- Centroid divides each median into a 2:1 ratio.
- Use the concept of finding other segment lengths based on given measures and relationships in the triangle.
Transcribed Image Text:**Text:** Given the diagram below, if \( H \) is the centroid of \( \triangle BCD \), \( BG = 86 \), \( CD = 34 \), \( EH = 15 \), and \( CF = 39 \), find each measure. Round answers to the nearest tenth when needed. **Diagram Explanation:** The diagram depicts triangle \( \triangle BCD \) with centroid \( H \). The centroid is the point where the medians of the triangle intersect. Medians are line segments drawn from a vertex to the midpoint of the opposite side. Points \( E \), \( F \), and \( G \) represent midpoints of sides \( BC \), \( BD \), and \( CD \) respectively. The following line segments are given or need to be determined: - \( GD \) = ________ - \( HG \) = ________ - \( BH \) = ________ - \( CH \) = ________ - \( HF \) = ________ - \( ED \) = ________ **Known Values:** - \( BG = 86 \) - \( CD = 34 \) - \( EH = 15 \) - \( CF = 39 \) **Concepts to Use:** - Centroid divides each median into a 2:1 ratio. - Use the concept of finding other segment lengths based on given measures and relationships in the triangle.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Knowledge Booster
Sample space, Events, and Basic Rules of Probability
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning