Question

∠eif ≅ ∠fig. complete the proof that ↔{fh} ⊥ ↔{eg}.

Explanation:

Step1: Definition of supplementary angles

$\angle EIF$ and $\angle FIG$ are adjacent angles that form a linear pair. By the definition of supplementary angles, $m\angle EIF + m\angle FIG=180^{\circ}$.

Step2: Substitution property of equality

Since $\angle EIF\cong\angle FIG$, then $m\angle EIF = m\angle FIG$. Substitute $m\angle FIG$ with $m\angle EIF$ in the equation $m\angle EIF + m\angle FIG = 180^{\circ}$, we get $m\angle EIF+m\angle EIF = 180^{\circ}$.

Step3: Definition of perpendicular lines

If the measure of an angle formed by two lines is $90^{\circ}$, then the two lines are perpendicular. Since $m\angle EIF = 90^{\circ}$, by the definition of perpendicular lines, $\overleftrightarrow{FH}\perp\overleftrightarrow{EG}$.

Answer:

1. Definition of supplementary angles; 3. Substitution property of equality; 5. Definition of perpendicular lines.