Question

complete the proof that ∠eif ≅ ∠gih.

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

Explanation:

Step1: Given linear - pair property

$\angle EIF$ and $\angle FIG$ form a linear pair, so $m\angle EIF + m\angle FIG=180^{\circ}$

Step2: Given linear - pair property

$\angle FIG$ and $\angle GIH$ form a linear pair, so $m\angle FIG + m\angle GIH = 180^{\circ}$

Step3: Transitive property of equality

Since $m\angle EIF + m\angle FIG=180^{\circ}$ and $m\angle FIG + m\angle GIH = 180^{\circ}$, we can say $m\angle EIF + m\angle FIG=m\angle FIG + m\angle GIH$

Step4: Subtraction property of equality

Subtract $m\angle FIG$ from both sides of the equation $m\angle EIF + m\angle FIG=m\angle FIG + m\angle GIH$. We get $m\angle EIF=m\angle GIH$

Step5: Definition of congruent angles

If two angles have equal measures, they are congruent. So $\angle EIF\cong\angle GIH$

Answer:

$\angle EIF\cong\angle GIH$ because they have equal measures as shown by the linear - pair and equality properties.