   Chapter 5.4, Problem 41E 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 the figure, square RSTV has its vertices on the sides of square WXYZ as shown. If ZT=5 and TY=12 find TS. Also find RT. To determine

To Find:

The length of TS and RT.

Explanation

Given In the figure, square RSTV has its vertices on the sides of square WXYZ as shown. If ZT=5 and TY=12.

Since WXYZ is a square, we obtain Y and Z are right angles. So,

mY=mZ=900.

And since RSTV is also a square, VTS is a right angle VTS=900,

By the Angle-Addition Postulate we see,

mZTY=mVTS+mVTZ+mSTY         =900+mVTZ+mSTY         =1800

The sum of angles in a triangle is 1800.

From ΔSYT

mSTY+mTSY+mY=1800mSTY+mTSY+900=1800mSTY+mTSY=900,

Then,

mYST=mZTV

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