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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 7.1, Problem 44E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Note: Exercises preceded by an asterisk are of a more challenging nature.

In Exercises 39 and 42, refer to the line segments shown.

Use the following theorem to construct the geometric mean of the numerical lengths of the segments W X - and Y Z - .

Theorem: The length of the altitude to the hypotenuse of a right triangle is the geometric mean between the lengths of the segments of the hypotenuse.

Chapter 7.1, Problem 44E, Note: Exercises preceded by an asterisk are of a more challenging nature. In Exercises 39 and 42,

To determine

To construct:

The geometric mean of the numerical lengths of the segments WX- and YZ-.

Explanation

Theorem:

Geometric mean theorem:

The length of the altitude to the hypotenuse of a right triangle is the geometric mean between the lengths of the segments of the hypotenuse.

Calculation:

Consider a right angle triangle WXZ which consists of two right triangles WXY and WYZ as shown in figure.

Consider the right triangles WXY and WXZ.

XYWX=WXXZ

Consider the right triangles WXY and WYZ.

XYWY=WYWZ

Consider the right triangles WYZ and WXZ.

WZWY=XZWZ

From the above, we find that the length of the altitude to the hypotenuse of a right triangle is the geometric mean between the lengths of the segments of the hypotenuse

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Chapter 7.1,
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Sect-7.1 P-1ESect-7.1 P-2ESect-7.1 P-3ESect-7.1 P-4ESect-7.1 P-5ESect-7.1 P-6ESect-7.1 P-7ESect-7.1 P-8ESect-7.1 P-9ESect-7.1 P-10E
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