Question

complete the proof by choosing the correct
eason\. given: $mangle qps = mangle vpt$, $mangle1 = mangle3$. prove: $mangle2 = mangle4$. statement reason 1 $mangle qps = mangle1 + mangle2$ reason ? 2 $mangle vpt = mangle3 + mangle4$ reason ? 3 $mangle qps = mangle vpt$ reason ? 4 $mangle1 + mangle2 = mangle3 + mangle4$ reason ? 5 $mangle1 = mangle3$ reason ? 6 $mangle3 + mangle2 = mangle3 + mangle4$ reason ? 7 $mangle2 = mangle4$ reason ?

Explanation:

Step1: Angle - addition postulate

The measure of an angle formed by two non - collinear rays with a common endpoint is the sum of the measures of the two adjacent angles that make it up. So, $m\angle QPS=m\angle1 + m\angle2$ and $m\angle VPT=m\angle3 + m\angle4$ because of the angle - addition postulate.

Step2: Given

We are given in the problem statement that $m\angle QPS = m\angle VPT$.

Step3: Substitution property of equality

Since $m\angle QPS=m\angle1 + m\angle2$, $m\angle VPT=m\angle3 + m\angle4$ and $m\angle QPS = m\angle VPT$, we can substitute to get $m\angle1 + m\angle2=m\angle3 + m\angle4$.

Step4: Given

We are given that $m\angle1 = m\angle3$.

Step5: Substitution property of equality

Substitute $m\angle1$ with $m\angle3$ in the equation $m\angle1 + m\angle2=m\angle3 + m\angle4$ to get $m\angle3 + m\angle2=m\angle3 + m\angle4$.

Step6: Subtraction property of equality

Subtract $m\angle3$ from both sides of the equation $m\angle3 + m\angle2=m\angle3 + m\angle4$. We get $m\angle2 = m\angle4$.

Answer:

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