Chapter 9, Problem 28CUR

(a)

To determine

To Complete: the statement $\Delta RWZ=\underset{\_}{?}$ in the figure shown.

Answer to Problem 28CUR

  $\Delta ZWS$

Explanation of Solution

Given:

Figure is shown below.

  

Calculation:

In $\Delta RWZ\text{ and }\Delta ZWS$ .

  $\begin{array}{l}\angle WRZ\cong \angle WZS\therefore \left(\text{Given}\right)\\ \angle W\cong \angle W\therefore \left(\text{Common}\right)\\ WZ\cong WZ\therefore \left(\text{Common}\right)\end{array}$

By AAS similarity, $\Delta RWZ\sim \Delta ZWS$ .

Therefore, the answer is $\Delta ZWS$ .

(b)

To determine

To Complete: the statement $\frac{RW}{\underset{\_}{?}}=\frac{ZR}{\underset{\_}{?}}=\frac{WZ}{\underset{\_}{?}}$ in the figure shown.

Answer to Problem 28CUR

  $ZW,SZ\text{ and }WS$

Explanation of Solution

Given:

Figure is shown below.

  

Calculation:

In $\Delta RWZ\text{ and }\Delta ZWS$ .

  $\begin{array}{l}\angle WRZ\cong \angle WZS\therefore \left(\text{Given}\right)\\ \angle W\cong \angle W\therefore \left(\text{Common}\right)\\ WZ\cong WZ\therefore \left(\text{Common}\right)\end{array}$

By AAS similarity, $\Delta RWZ\sim \Delta ZWS$ .

Therefore,

  $\frac{RW}{ZW}=\frac{ZR}{SZ}=\frac{WZ}{WS}$

Therefore, the answer is $ZW,SZ\text{ and }WS$ .

(c)

To determine

To Complete: the statement $WZ=\underset{\_}{?}\text{and }RS=\underset{\_}{?}$ in the figure shown.

Answer to Problem 28CUR

  $12\text{ and }5.4$

Explanation of Solution

Given:

Figure is shown below.

  

  $RW=15,ZR=10\text{and }ZS=8$

Calculation:

In $\Delta RWZ\text{ and }\Delta ZWS$ .

  $\begin{array}{l}\angle WRZ\cong \angle WZS\therefore \left(\text{Given}\right)\\ \angle W\cong \angle W\therefore \left(\text{Common}\right)\\ WZ\cong WZ\therefore \left(\text{Common}\right)\end{array}$

By AAS similarity, $\Delta RWZ\sim \Delta ZWS$ .

Therefore,

  $\begin{array}{l}\frac{RW}{ZW}=\frac{ZR}{SZ}=\frac{WZ}{WS}\\ \frac{15}{ZW}=\frac{10}{8}\\ ZW=\frac{15\times 8}{10}\\ ZW=12\end{array}$

  $\begin{array}{l}\frac{ZR}{SZ}=\frac{WZ}{WS}\\ \frac{10}{8}=\frac{12}{WS}\\ WS=\frac{12\times 8}{10}\\ WS=9.6\end{array}$

And

  $\begin{array}{l}RS=RW-SW\\ RS=15-9.6\\ RS=5.4\end{array}$

Therefore, the answer is $12\text{ and }5.4$ .