Question

Copy everything shown and supply missing statements and reasons.

Given:$ST=RN$;$IT=RU$

Prove: $SI=UN$

Proof;

Short answer

From the given figure, it can be observed that some of $SI$and $IT$gives $ST$, that is $ST=SI+IT$.

From the given figure, it can be observed that some of $RU$and $UN$gives $RN$, that is $RU+UN=RN$.

Step-by-step solution

Step 1. Apply segment addition postulate.

From the given figure, it can be observed that some of $SI$and $IT$gives $ST$, that is $ST=SI+IT$.

From the given figure, it can be observed that some of $RU$and $UN$gives $RN$, that is $RU+UN=RN$.

Step 2. Apply Substitution property.

Substitute $SI+IT$for $ST$and $RU+UN$for $RN$in $ST=RN$.

$\begin{array}{c}ST=RN\\ SI+IT=RU+UN\end{array}$

Step 3. Apply subtraction property of algebra to step 2.

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

$\begin{array}{c}SI+IT=IT+UN\\ SI=UN\end{array}$

Hence it is proved that $SI=UN$.