Chapter 8, Problem 5CA

To determine

To explain: that $\overrightarrow{AG}$ is the angle bisector of $\angle CAB$ using the steps in the construction.

Answer to Problem 5CA

  $3$ steps of using angle divider can make the new angle.

Explanation of Solution

Given:

  

Concept used:

A line that splits an angle into two equal angles.

The interior or bisector of an angle, also called the internal angle bisector is the line or line segment that divides the angle into two equal parts.

Calculation:

Step $1$ : the compass is opened to a certain length and it is fixed end of the compass is placed on $A$ and two arcs are made on both of the given lines, subtending the given angle. These arcs $B\text{ and }C$ .

Step $2$ : without changing this length, the fixed point is placed on $B$ and a third arc is drawn. Then the fixed point is placed on $C$ and a fourth arc is drawn. These arcs should intersect at arc certain point.

Step $3$ : join $A$ and the point of intersection of the $2$ arcs $G$ to make the angle bisector of $\angle CAB$ .

Hence, $3$ steps of using angle divider can make the new angle.