Chapter 6.1, Problem 4WE

Solution

(a)

To show: whether the statement $RT>RS$ can be deduced shown in figure in yes or no.

yes

Given:

Figure is shown below.

  

  $m\angle RVS=m\angle RSV=65$

Calculation:

Using property .

If $a=b+c\text{ and }c>0,\text{then }a>b$

  $\begin{array}{l}RT=RS+ST\\ \therefore RT>RS\end{array}$

Therefore, the answer is yes.

(c)

To show: whether the statement $RT>RV$ can be deduced shown in figure in yes or no.

yes

Given:

Figure is shown below.

  

  $m\angle RVS=m\angle RSV=65$

Calculation:

Using property .

If $a=b+c\text{ and }c>0,\text{then }a>b$

  $\begin{array}{l}RT=RS+ST\\ \therefore RT>RS\end{array}$

Since, $m\angle RVS=m\angle RSV=65$ therefore using property of sides opposite to equal angles are also equal.

  $\begin{array}{l}\therefore RV=RS\\ \Rightarrow RT>RS\\ \Rightarrow RT>RV\end{array}$

Therefore, the answer is yes.

(c)

To Tell: whether the statement $RS>ST$ can be deduced shown in figure in yes or no.

No

Given:

Figure is shown below.

  

  $m\angle RVS=m\angle RSV=65$

Calculation:

Using property .

If $a=b+c\text{ and }c>0,\text{then }a>b$

  $\begin{array}{l}RT=RS+ST\\ \therefore RT>RS\end{array}$

For $RS>ST$ ,data are insufficient.

Therefore, the answer is no.

(d)To Tell: whether the statement $VT<RS$ can be deduced shown in figure in yes or no.

No

Given:

Figure is shown below.

  

  $m\angle RVS=m\angle RSV=65$

Calculation:

For $VT<RS$ ,data are insufficient.

Therefore, the answer is no.