Question

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

Explanation:

Step1: Angle - addition postulate

The measure of an angle formed by two adjacent angles is the sum of the measures of the two adjacent angles. So, $m\angle CGE=m\angle1 + m\angle2$.

Step2: Angle - addition postulate

Similarly, for $\angle FGD$, $m\angle FGD=m\angle2 + m\angle3$ because of the angle - addition postulate.

Step3: Given

It is given in the problem statement that $m\angle CGE = m\angle FGD$.

Step4: Substitution property

Since $m\angle CGE=m\angle1 + m\angle2$, $m\angle FGD=m\angle2 + m\angle3$ and $m\angle CGE = m\angle FGD$, we can substitute to get $m\angle1 + m\angle2=m\angle2 + m\angle3$.

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
5. Subtraction property of equality