   Chapter 5.4, Problem 5E 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 5.4.2 to find RV if S V = 6     and V T = 8 . Exercises 1-6

To determine

To Find:

The length of RV.

Explanation

Given SV=6 and VT= 8

And figure,

From the figure,

ΔRST is a right triangle with right angle RST, SV¯RT¯

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

VTSV=SVRV

Recall the Means-Extremes Property

In a proportion, the product of the means equals the product of the extremes. That is,

If ab=cd then ad= bc

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