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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∠RVS=m∠RSV=65.

a. RT>RS

b. RT>RV

c. RS>ST

d. VT<RS

Short Answer

Expert verified

Use the diagram given for angles as shown below

Step by step solution

01

a.Step 1 - Draw diagram 

Use the diagram given for angles as shown below

02

– Inequality property 

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

03

– Check the given statement RT>RS

As from the figure RS+ST=RThence RT>RS.

So, the answer is Yes.

04

b.Step 1 – Property of angles of a triangle

Property of sides opposite to equal angles is also equal.

05

– Check sides RV and VS 

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

06

– Check the given statement 

Since RV=RSand RT>RS therefore RT>RV.

Thus, the answer is Yes.

07

c.Step 1 - Draw diagram 

Use the diagram given for angles as shown below

08

– check sides RS and ST 

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

09

- Check the given statement

Since RS+ST=RTand RT>RStherefore data are insufficient for RS>ST

Thus, the answer is No.

10

d.Step 1 – Inequality property 

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

11

– Use result of part (b) 

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

12

- Check the given statement 

Since RS+ST=RTand RT>RStherefore data are insufficient for VT<RS

Thus, the answer is No.

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