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Chapter 2: Q12 (page 42)

Copy everything shown and write a two-column proof.

Given: RP=TQ;

PS=QS

Prove:RS=TS

Short Answer

Expert verified

Statements

Reasons

1.RP=TQ;PS=QS

Given

2.RP+PS=TQ+QS

2. Addition property

3.RS=RP+PS;TS=TQ+QS

3. Segment addition postulate

4.RS=TS

4. Substitution property

Step by step solution

01

Step 1. Apply the addition property of algebra.

If a=band c=d, then a+c=b+d.

RP+PS=TQ+QS

02

Step 2. Apply segment addition postulate.

From the given figure, it can be observed that sum of RPand PSgives RS, that is RS=RP+PS.

From the given figure, it can be observed that sum of TQand QSgives TS, that is TS=TQ+QS.

03

Step 3. Apply Substitution property.

Substitute RSfor RP+PSand TSfor TQ+QSin step 1.

RP+PS=TQ+QSRS=TS

Hence, it is proved that RS=TS.

04

Step 4. Write a two-column proof.

Write a two-column proof with the help of the above-mentioned steps.

Statements

Reasons

1.RP=TQ;PS=QS

Given

2.RP+PS=TQ+QS

2. Addition property

3.RS=RP+PS;TS=TQ+QS

3. Segment addition postulate

4.RS=TS

4. Substitution property

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Most popular questions from this chapter

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.

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State the converse of each conditional. Is the converse true or false?

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Provide a counterexample to show that each statement is false.

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(4) s or r

Copy everything shown and write a two-column proof.

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