Question

Some information about the diagram is given. Tell whether the other statements can be deduced from what is given. (Write Yes or No).

Given: $m\angle RVS=m\angle RSV=65$.

a. $RT>RS$

b. $RT>RV$

c. $RS>ST$

d. $VT<RS$

Short answer

Use the diagram given for angles as shown below

Step-by-step solution

a.Step 1 - Draw diagram 

Use the diagram given for angles as shown below

– Inequality property 

If $a=b+c$ and $c>0$ then $a>c$.

– Check the given statement RT>RS

As from the figure $RS+ST=RT$hence $RT>RS$.

So, the answer is Yes.

b.Step 1 – Property of angles of a triangle

Property of sides opposite to equal angles is also equal.

– Check sides RV and VS 

Since given that $m\angle RVS=m\angle RSV=65$therefore from the property of sides opposite to equal angles are also equal $RV=RS$.

– Check the given statement 

Since $RV=RS$and $RT>RS$ therefore $RT>RV$.

Thus, the answer is Yes.

c.Step 1 - Draw diagram 

Use the diagram given for angles as shown below

– check sides RS and ST 

Use part (b) as shown that point $m\angle RVS=m\angle RSV=65$and $RV=RS$.

- Check the given statement

Since $RS+ST=RT$and $RT>RS$therefore data are insufficient for $RS>ST$

Thus, the answer is No.

d.Step 1 – Inequality property 

If $a=b+c$ and $c>0$ then $a>c$.

– Use result of part (b) 

Use part (b) as shown that $m\angle RVS=m\angle RSV=65$therefore from the property of sides opposite to equal angles are also equal $RV=RS$.

- Check the given statement 

Since $RS+ST=RT$and $RT>RS$therefore data are insufficient for $VT<RS$

Thus, the answer is No.