Question

complete the proof by choosing the correct
eason\. given: (mangle efg = mangle jhg), (mangle1 = mangle3). prove: (mangle2 = mangle4). statement reason 1 (mangle efg = mangle1 + mangle2) reason? 2 (mangle jhg = mangle3 + mangle4) reason? 3 (mangle efg = mangle jhg) 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

By the angle - addition postulate, if a ray divides an angle into two non - overlapping angles, the measure of the whole angle is the sum of the measures of the two smaller angles. So, $m\angle EFG=m\angle1 + m\angle2$ and $m\angle JHG=m\angle3 + m\angle4$.

Step2: Given

The problem states that $m\angle EFG=m\angle JHG$.

Step3: Substitution property of equality

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

Step4: Given

The problem states 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