Chapter 8.2, Problem 65SPR

To determine

To prove: $FH>FG$

Explanation of Solution

Given information: It is given that $FG\perp l$ . $\overline{FH}$ is any non-perpendicular segment from $F$ to $l$ .

Proof:

Since perpendicular line form a right angle,

  $\therefore \angle 2=90°$

By using Triangle Sum Theorem,

  $\angle 2+\angle 3+\angle F=180°$

Substitution Property of Equality,

  $90°+\angle 3+\angle F=180°$

Subtraction Property of Equality,

  $\angle 3+\angle F=90°$

Substitute $90°=\angle 2$ ,

  $\angle 3+\angle F=\angle 2$

  $\therefore \angle 2>\angle 3$

By Hinge Theorem,

  $FH>FG$

Hence, proved.