   Chapter 5.6, Problem 24E 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

In right Δ R S T (not shown) with right ∠ S , R V → bisects ∠ S R T so that V lies on side S T ¯ . If R S = 6 , S T = 6 3 , and R T = 12 find S V and V T .

To determine

To find:

SV and VT.

Explanation

Given:

In right ΔRST with right S, RV bisects SRT so that V lies on side ST¯. Also RS=6,ST=63,RT=12.

Theorem used:

Angle bisector theorem:

If a ray bisects one angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the two sides that form the bisected angle.

Calculation:

In right ΔRST, RV bisects SRT.

By angle bisector theorem, we get

SRRT=SVVT.

We know that, if ab=cd then a+bb=c+dd.

SR+RTRT=SV+VTVT

SR+RTRT=STVT

Given that RS=6,ST=63,RT=12

Thus 6+1212=63VT

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