Question

complete the proof that ∠gih≅∠eif.
statement

1. m∠eif + m∠fig = 180°
2. m∠fig + m∠gih = 180°
3. m∠eif + m∠fig = m∠fig + m∠gih
4. m∠eif = m∠gih
5. ∠gih≅∠eif

reason
angles forming a linear pair sum to 180°
transitive property of equality
properties of addition, subtraction, multiplication, and division
definition of congruence

Explanation:

Step1: Identify linear - pair property

Angles $\angle FIG$ and $\angle GIH$ form a linear pair. Since angles forming a linear pair sum to $180^{\circ}$, we have $m\angle FIG + m\angle GIH=180^{\circ}$.

Step2: Use transitive property

We know $m\angle EIF + m\angle FIG = 180^{\circ}$ and $m\angle FIG + m\angle GIH = 180^{\circ}$. By the transitive property of equality, $m\angle EIF + m\angle FIG=m\angle FIG + m\angle GIH$.

Step3: Apply subtraction property

Subtract $m\angle FIG$ from both sides of the equation $m\angle EIF + m\angle FIG=m\angle FIG + m\angle GIH$. According to the subtraction property of equality, we get $m\angle EIF=m\angle GIH$.

Step4: Use congruence definition

Since $m\angle EIF = m\angle GIH$, by the definition of congruence (if two angles have the same measure, they are congruent), $\angle GIH\cong\angle EIF$.

Answer:

The reason for step 2 is "Angles forming a linear pair sum to 180°" as $\angle FIG$ and $\angle GIH$ form a linear - pair.