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
which sequence puts the steps in the correct order to prove that ∠feg≅∠hei?
3,6,4,2,1,5
3,4,6,2,1,5
3,1,4,2,6,5
3,4,1,2,6,5

Explanation:

Step1: Start with given

We start with the given information $\angle FEH\cong\angle GEI$. So the first step is statement 3.

Step2: Use congruence - definition

By the definition of congruence, if $\angle FEH\cong\angle GEI$, then $m\angle FEH = m\angle GEI$. So the second step is statement 6.

Step3: Apply angle - addition postulate

We know from the angle - addition postulate that $m\angle FEH=m\angle FEG + m\angle GEH$ and $m\angle GEI=m\angle HEI + m\angle GEH$. So the third step is statement 4.

Step4: Use substitution

Substitute the expressions from step 3 into the equation from step 2, we get $m\angle FEG + m\angle GEH=m\angle HEI + m\angle GEH$. So the fourth step is statement 2.

Step5: Apply subtraction property

Using the subtraction property of equality, subtract $m\angle GEH$ from both sides of the equation in step 4 to get $m\angle FEG=m\angle HEI$. So the fifth step is statement 1.

Step6: Use congruence - definition again

By the definition of congruence, if $m\angle FEG=m\angle HEI$, then $\angle FEG\cong\angle HEI$. So the sixth step is statement 5.

Answer:

3, 6, 4, 2, 1, 5