Question

Copy everything shown and supply missing statements and reasons.

Given: $DW=ON$

Prove: $DO=WN$

Proof:

Short answer

From the given figure, it can be observed that some of $DO$and $OW$gives $DW$, that is $DW=DO+OW$.

From the given figure, it can be observed that some of $OW$and $WN$gives $ON$, that is $ON=OW+WN$.

Step-by-step solution

Step 1. Apply segment addition postulate.

From the given figure, it can be observed that some of $DO$and $OW$gives $DW$, that is $DW=DO+OW$.

From the given figure, it can be observed that some of $OW$and $WN$gives $ON$, that is $ON=OW+WN$.

Step 2. Apply Substitution property.

Substitute $DO+OW$for $DW$and $OW+WN$for $ON$in $DW=ON$.

$\begin{array}{c}DW=ON\\ DO+OW=OW+WN\end{array}$

Step 3. Reflexive property of congruence.

By reflexive property, $OW=OW$.

Step 4. Apply subtraction property of algebra to step 2.

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

$\begin{array}{c}DO+OW=OW+WN\\ DO=WN\end{array}$

Hence, it is proved that $DO=WN$.