   Chapter 7.1, Problem 46E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

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. 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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