Question

complete the proof that $overleftrightarrow{fh}perpoverleftrightarrow{eg}$. statement reason 1 $angle eifcongangle fig$ given 2 $mangle eif + mangle fig=180^{circ}$ angles forming a linear pair sum to $180^{circ}$ 3 $mangle eif + mangle eif=180^{circ}$ 4 $mangle eif = 90^{circ}$ properties of addition, subtraction, multiplication, and division 5 $overleftrightarrow{fh}perpoverleftrightarrow{eg}$ definition of perpendicular lines

Explanation:

Step1: Substitute equal - angle measures

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

Step2: Solve for $m\angle EIF$

Given $m\angle EIF + m\angle EIF = 180^{\circ}$, which is $2m\angle EIF=180^{\circ}$. Dividing both sides of the equation by 2 gives $m\angle EIF = 90^{\circ}$.

Step3: Use perpendicular - line definition

If the angle between two lines is $90^{\circ}$, by the definition of perpendicular lines, $\overleftrightarrow{FH}\perp\overleftrightarrow{EG}$.

Answer:

The reason for step 3 is "Substitution property of equality".