Chapter CSB1.9, Problem 1E

To determine

To construct: The angle bisector of the given figure.

Explanation of Solution

Given:

A figure is given as shown:

  

An angle bisector is the line segment, which divides the angle into two equal parts.

We need to bisect the $<XZY$

Place the compass point on the vertex of the angle, that is the point $Z$. Now, stretch the compass and draw arc such that the pencil crosses both $ZX$ and $ZY$ .

  

Now, we have two intersection points, those are $B$ and $A$ . Place the point of the compass on the intersection point $B$ and make an arc. Now, place the compass on the intersection point $A$ and make a similar arc.

  

The two small arcs in the interior of the angle should be intersecting. Let the intersection point is $C$ of the two arcs.

Connect the vertex the point $Z$ with the intersection point is $C$ of the arcs.

  

The line segment $ZD$ divides $<XZY$ into two equal angles $<XZD$ and $<YZD$ , each being half of the given angle $<XZY$