Question

Copy everything shown and write a two-column proof.

Given:$RQ=TP;$

$ZQ=ZP$

Prove:$RZ=TZ$

Short answer

Statements	Reasons
1.	Given
2.	2. Subtraction property
3.	3. Segment subtraction postulate
4.	4. Substitution property

Step-by-step solution

Step 1. Apply subtraction property of algebra.

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

$RQ-ZQ=TP-ZP$

Step 2. Apply segment subtraction postulate.

From the given figure, it can be observed that difference between $RQ$and $ZQ$gives $RZ$, that is $RZ=RQ-ZQ$.

From the given figure, it can be observed that difference between $TP$and $ZP$gives $TZ$, that is $TZ=TP-ZP$.

Step 3. Apply Substitution property.

Substitute $RZ$for $RQ-ZQ$and $TZ$for $TP-ZP$in step 1.

$\begin{array}{c}RQ-ZQ=TP-ZP\\ RZ=TZ\end{array}$

Hence, it is proved that $RZ=TZ$.

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.$RQ-ZQ=TP-ZP$	2. Subtraction property
3.$\begin{array}{c}RZ=RQ-ZQ;\\ TZ=TP-ZP\end{array}$	3. Segment subtraction postulate
4.$RZ=TZ$	4. Substitution property