Question

Copy everything shown and write a two-column proof.

Given:$m\angle 1=m\angle 2;$

$m\angle 3=m\angle 4;$

Prove:$m\angle SRT=m\angle STR$

Short answer

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

$m\angle 1+m\angle 3=m\angle 2+m\angle 4$

Step-by-step solution

Step 1. Apply the addition property of algebra.

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

$m\angle 1+m\angle 3=m\angle 2+m\angle 4$

Step 2. Angle addition postulate.

From the given figure, it can be observed that some of $m\angle 1$and $m\angle 3$gives $m\angle SRT$, that is $m\angle 2+m\angle 4=m\angle STR$.

From the given figure, it can be observed that some of $m\angle 2$and $m\angle 4$gives $m\angle STR$, that is $m\angle 2+m\angle 4=m\angle STR$.

Step 3. Apply substitution property.

Substitute $m\angle SRT$for $m\angle 1+m\angle 3$and $m\angle STR$for $m\angle 2+m\angle 4$in step 1.

$\begin{array}{c}m\angle 1+m\angle 3=m\angle 2+m\angle 4\\ m\angle SRT=m\angle STR\end{array}$

Step 4. Write a two-column proof.

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