Question

complete the proof by choosing the correct
eason\. given: m∠ptr = m∠stq prove: m∠1 = m∠3 statement reason 1 m∠ptr = m∠1 + m∠2 reason ? 2 m∠stq = m∠2 + m∠3 reason ? 3 m∠ptr = m∠stq reason ? 4 m∠1 + m∠2 = m∠2 + m∠3 reason ? 5 m∠1 = m∠3 reason ?

Explanation:

Step1: Angle - addition postulate

$m\angle PTR=m\angle1 + m\angle2$ because the measure of an angle formed by two non - collinear rays (in this case, the rays that form $\angle PTR$) is the sum of the measures of its non - overlapping sub - angles.

Step2: Angle - addition postulate

$m\angle STQ=m\angle2 + m\angle3$ for the same reason as step 1. The measure of $\angle STQ$ is the sum of the measures of its non - overlapping sub - angles.

Step3: Given

$m\angle PTR = m\angle STQ$ is given in the problem statement.

Step4: Substitution property of equality

Since $m\angle PTR=m\angle1 + m\angle2$ and $m\angle STQ=m\angle2 + m\angle3$ and $m\angle PTR = m\angle STQ$, we can substitute the expressions for $m\angle PTR$ and $m\angle STQ$.

Step5: Subtraction property of equality

Subtract $m\angle2$ from both sides of the equation $m\angle1 + m\angle2=m\angle2 + m\angle3$. We get $m\angle1=m\angle3$.

Answer:

1. Angle - addition postulate
2. Angle - addition postulate
3. Given
4. Substitution property of equality
5. Subtraction property of equality