Homework Help is Here – Start Your Trial Now!
Math
Geometry
**Right Triangle Relationships: Finding the True Proportion** In the accompanying diagram of right triangle \( ABC \), altitude \( BD \) is drawn to hypotenuse \( AC \). (Here, the diagram would show a right triangle \( ABC \) where \( \angle ABC \) is the right angle, and line segment \( BD \) extends perpendicularly from point \( B \) to segment \( AC \), where \( D \) lies on \( AC \)). **Problem:** Which statement must always be true? **Options:** A. \( \frac{AD}{AB} = \frac{AB}{AC} \) B. \( \frac{BD}{BC} = \frac{AB}{AD} \) C. \( \frac{AB}{BC} = \frac{BD}{AC} \) D. \( \frac{AD}{AB} = \frac{BC}{AC} \) The correct answer is option C. **Explanation:** In the context of the right triangle and the altitude drawn to the hypotenuse, several relationships involving similar triangles and geometric mean properties can be used. Here, statement C, \( \frac{AB}{BC} = \frac{BD}{AC} \), is derived based on the properties of similar triangles and the relationships of segments in a right triangle with an altitude drawn to the hypotenuse.

**Right Triangle Relationships: Finding the True Proportion** In the accompanying diagram of right triangle \( ABC \), altitude \( BD \) is drawn to hypotenuse \( AC \). (Here, the diagram would show a right triangle \( ABC \) where \( \angle ABC \) is the right angle, and line segment \( BD \) extends perpendicularly from point \( B \) to segment \( AC \), where \( D \) lies on \( AC \)). **Problem:** Which statement must always be true? **Options:** A. \( \frac{AD}{AB} = \frac{AB}{AC} \) B. \( \frac{BD}{BC} = \frac{AB}{AD} \) C. \( \frac{AB}{BC} = \frac{BD}{AC} \) D. \( \frac{AD}{AB} = \frac{BC}{AC} \) The correct answer is option C. **Explanation:** In the context of the right triangle and the altitude drawn to the hypotenuse, several relationships involving similar triangles and geometric mean properties can be used. Here, statement C, \( \frac{AB}{BC} = \frac{BD}{AC} \), is derived based on the properties of similar triangles and the relationships of segments in a right triangle with an altitude drawn to the hypotenuse.

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
See similar textbooks
icon
Related questions
Topic Video
Question

Quesiton 24

**Right Triangle Relationships: Finding the True Proportion** In the accompanying diagram of right triangle \( ABC \), altitude \( BD \) is drawn to hypotenuse \( AC \). (Here, the diagram would show a right triangle \( ABC \) where \( \angle ABC \) is the right angle, and line segment \( BD \) extends perpendicularly from point \( B \) to segment \( AC \), where \( D \) lies on \( AC \)). **Problem:** Which statement must always be true? **Options:** A. \( \frac{AD}{AB} = \frac{AB}{AC} \) B. \( \frac{BD}{BC} = \frac{AB}{AD} \) C. \( \frac{AB}{BC} = \frac{BD}{AC} \) D. \( \frac{AD}{AB} = \frac{BC}{AC} \) The correct answer is option C. **Explanation:** In the context of the right triangle and the altitude drawn to the hypotenuse, several relationships involving similar triangles and geometric mean properties can be used. Here, statement C, \( \frac{AB}{BC} = \frac{BD}{AC} \), is derived based on the properties of similar triangles and the relationships of segments in a right triangle with an altitude drawn to the hypotenuse.
Transcribed Image Text:**Right Triangle Relationships: Finding the True Proportion** In the accompanying diagram of right triangle \( ABC \), altitude \( BD \) is drawn to hypotenuse \( AC \). (Here, the diagram would show a right triangle \( ABC \) where \( \angle ABC \) is the right angle, and line segment \( BD \) extends perpendicularly from point \( B \) to segment \( AC \), where \( D \) lies on \( AC \)). **Problem:** Which statement must always be true? **Options:** A. \( \frac{AD}{AB} = \frac{AB}{AC} \) B. \( \frac{BD}{BC} = \frac{AB}{AD} \) C. \( \frac{AB}{BC} = \frac{BD}{AC} \) D. \( \frac{AD}{AB} = \frac{BC}{AC} \) The correct answer is option C. **Explanation:** In the context of the right triangle and the altitude drawn to the hypotenuse, several relationships involving similar triangles and geometric mean properties can be used. Here, statement C, \( \frac{AB}{BC} = \frac{BD}{AC} \), is derived based on the properties of similar triangles and the relationships of segments in a right triangle with an altitude drawn to the hypotenuse.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Propositional Calculus
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
SEE MORE TEXTBOOKS