Chapter 11.2, Problem 20PPS

a.

To determine

To find: congruence statement involving a pair of corresponding sides

Answer to Problem 20PPS

  $\begin{array}{l}\Delta YWX\cong \Delta YWZ\\ YW=YW,WX=WZ,YX=YZ\end{array}$

Explanation of Solution

Given information:The figure consists of a roof containing two congruent triangles

  

In $\Delta YWX$ and $\Delta YWZ$ ,

  $YX=YZ$ (Given)

  $XW=WZ$ (Given)

  $\angle YWX=\angle YWZ=90°$

So,

  $\Delta YWX\cong \Delta YWZ$ (using RHS congruence criteria)

As corresponding sides of the congruent triangles are equal,

  $YW=YW,WX=WZ,YX=YZ$

b.

To determine

To calculate : Distance from the right side of the roof to the center

Answer to Problem 20PPS

Distance from the right side of the roof to the center = 7 feet

Explanation of Solution

As $WZ=XW$ , $XW=\frac{1}{2}XZ$

  $XZ=14$ feet

So,

  $WZ=XW=\frac{1}{2}XZ=\frac{1}{2}(14)=7ft$

Here, WZ denotes distance from the right side of the roof at the base to the center.

So,name of the side = WZ

c.

To determine

To calculate : Length of WY

Answer to Problem 20PPS

  $WY=3feet$

Explanation of Solution

Formula used : Use $XW=WY+4$

Calculation :

  $XW=WY+4$

As $XW=7ft$ ,

  $\begin{array}{l}7=WY+4\\ \Rightarrow WY=7-4=3ft\end{array}$