Question

the two - column proof shown includes statements and reasons that are not in the correct order to prove that ∠feg≅∠hei.
step #\tstatement\treason
1.\tm∠feg = m∠hei\tsubtraction property of equality
2.\tm∠feg + m∠geh = m∠hei + m∠geh\tsubstitution property of equality
3.\t∠feh≅∠gei\tgiven
4.\tm∠feh = m∠feg + m∠geh and m∠gei = m∠hei + m∠geh\tangle addition postulate
5.\t∠feg≅∠hei\tdefinition of congruence
6.\tm∠feh = m∠gei\tdefinition of congruence

Explanation:

Step1: Start with given

We start with the given $\angle FEH\cong\angle GEI$. By the definition of congruence, we have $m\angle FEH = m\angle GEI$ (Step 6).

Step2: Apply Angle - Addition Postulate

Using the Angle - Addition Postulate, we know that $m\angle FEH=m\angle FEG + m\angle GEH$ and $m\angle GEI=m\angle HEI + m\angle GEH$ (Step 4).

Step3: Use Substitution Property

Substitute the expressions from Step 2 into the equation from Step 1. We get $m\angle FEG + m\angle GEH=m\angle HEI + m\angle GEH$ (Step 2).

Step4: Use Subtraction Property

Subtract $m\angle GEH$ from both sides of the equation in Step 3. By the Subtraction Property of Equality, we have $m\angle FEG=m\angle HEI$ (Step 1).

Step5: Prove congruence

Since $m\angle FEG = m\angle HEI$, by the definition of congruence, $\angle FEG\cong\angle HEI$ (Step 5).

The correct order of steps is:
3, 6, 4, 2, 1, 5

Answer:

3, 6, 4, 2, 1, 5