Question

an incomplete two - column proof shown includes some statements and reasons to prove ∠feg≅∠hei. complete each missing statement.
step #\tstatement\treason
1.\t∠feh≅∠gei\tgiven
2.\tm∠feh = \tdefinition of congruence
3.\tm∠feh=m∠feg + m∠geh and m∠gei = \tangle addition postulate
4.\tm∠feg+\t=m∠hei + m∠geh\tsubstitution property of equality
5.\tm∠feg=\tsubtraction property of equality
6.\t∠feg≅∠hei\tdefinition of congruence

Explanation:

Step1: Apply congruence definition

By the definition of congruence, if $\angle FEH\cong\angle GEI$, then $m\angle FEH = m\angle GEI$.

Step2: Use angle - addition postulate

The angle - addition postulate states that $m\angle GEI=m\angle HEI + m\angle GEH$.

Step3: Substitute equal - angle measures

Since $m\angle FEH = m\angle GEI$, and $m\angle FEH = m\angle FEG + m\angle GEH$ and $m\angle GEI=m\angle HEI + m\angle GEH$, we substitute to get $m\angle FEG + m\angle GEH=m\angle HEI + m\angle GEH$.

Step4: Apply subtraction property of equality

Subtracting $m\angle GEH$ from both sides of the equation $m\angle FEG + m\angle GEH=m\angle HEI + m\angle GEH$ gives $m\angle FEG=m\angle HEI$.

Answer:

Step #	Statement	Reason
3.	$m\angle GEI=m\angle HEI + m\angle GEH$	Angle Addition Postulate
4.	$m\angle FEG + m\angle GEH=m\angle HEI + m\angle GEH$	Substitution Property of Equality
5.	$m\angle FEG=m\angle HEI$	Subtraction Property of Equality