Question

Copy everything shown and write a two-column proof.

Given:$m\angle SRT=m\angle STR;$

$m\angle 3=m\angle 4$

Proof:$m\angle 1=m\angle 2$

Short answer

Statements	Reasons
1.	Given
2.	2. Angle addition postulate
3.	3. Substitution property
4.	4. Given
5.	5. Subtraction property

Step-by-step solution

Step 1. Angle addition postulate.

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

Step 2. Apply substitution property.

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

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

Step 3. Apply the subtraction property of algebra.

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

$m\angle 1=m\angle 2$

Step 4. Write a two-column proof.

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

Statements	Reasons
1.$m\angle SRT=m\angle STR$	Given
2.$\begin{array}{c}m\angle 1+m\angle 3=m\angle SRT;\\ m\angle 2+m\angle 4=m\angle STR\end{array}$	2. Angle addition postulate
3.$m\angle 1+m\angle 3=m\angle 2+m\angle 4$	3. Substitution property
4.$m\angle 3=m\angle 4$	4. Given
5.$m\angle 1=m\angle 2$	5. Subtraction property