   Chapter 5.4, Problem 4E 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

Use theorem 5.4.3 to form a proportion in which TS is a geometric mean.[Hint: Δ T V S ∼ Δ T S R ] Exercises 1-6

To determine

To Find:

Proportion in which TS is the geometric mean.

Explanation

Given:

From the figure,

ΔRST is a right triangle with right angle RST, and SV¯ is the altitude to hypotenuse TR¯.

From the theorem,

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

Since ΔRVSΔRST

Corresponding sides of similar triangles are proportional (CSSTP)

So, we have

VTTS=TSRT

Recall the Means-Extremes Property

In a proportion, the product of the means equals the product of the extremes

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