Chapter 8.5, Problem 55E

To determine

To Explain: The process of bisecting an angle and comparing it to bisecting a segment.

Explanation of Solution

Given information: The angle is bisected.

The following process or method is used to bisect an angle.

  

• First, fix the compass length and placed it on Point O.
• Make two arcs A and B on line OP and OQ.
• Place the compass on the arc A and B, respectively. And draw a new arc M.
• Join the arc M and Point O with a line OX.
• The bisector OX bisects the angle $\angle POQ$ in two equal halves.

Now, the following method is used to bisect a segment.

  

• Let $n$ units be the length of the line segment AB.
• Open a compass to a length greater than $\frac{n}{2}$ .
• Place the fixed end of the compass on the Point A and B, respectively. And draw arcs on both sides of segment AB.
• Join both points and make perpendicular bisector of the line AB.