Question

Copy everything shown and write a two-column proof.

Given: $RP=TQ;$

$PS=QS$

Prove:$RS=TS$

Short answer

Statements	Reasons
1.$\begin{array}{c}RP=TQ;\\ PS=QS\end{array}$	Given
2.$RP+PS=TQ+QS$	2. Addition property
3.$\begin{array}{c}RS=RP+PS;\\ TS=TQ+QS\end{array}$	3. Segment addition postulate
4.$RS=TS$	4. Substitution property

Step-by-step solution

Step 1. Apply the addition property of algebra.

If $a=b$and $c=d$, then $a+c=b+d$.

$RP+PS=TQ+QS$

Step 2. Apply segment addition postulate.

From the given figure, it can be observed that sum of $RP$and $PS$gives $RS$, that is $RS=RP+PS$.

From the given figure, it can be observed that sum of $TQ$and $QS$gives $TS$, that is $TS=TQ+QS$.

Step 3. Apply Substitution property.

Substitute $RS$for $RP+PS$and $TS$for $TQ+QS$in step 1.

$\begin{array}{c}RP+PS=TQ+QS\\ RS=TS\end{array}$

Hence, it is proved that $RS=TS$.

Step 4. Write a two-column proof.

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

Statements	Reasons
1.$\begin{array}{c}RP=TQ;\\ PS=QS\end{array}$	Given
2.$RP+PS=TQ+QS$	2. Addition property
3.$\begin{array}{c}RS=RP+PS;\\ TS=TQ+QS\end{array}$	3. Segment addition postulate
4.$RS=TS$	4. Substitution property