Chapter CSB1.9, Problem 3E

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 $<SZY$

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 $ZS$ and $ZY$ .

  

Now, we have two intersection points, those are $F$ and $G$ .

Place the point of the compass on the intersection point $F$ and make an arc. Now, place the compass on the intersection point $G$ and make a similar arc.

  

The two small arcs should be intersecting. Let the intersection point is $H$ of the two arcs.

Connect the vertex the point $Z$ with the intersection point is $H$ .

  

The line segment $ZM$ divides $<SZY$ into two equal angles $<SZM$ and $<YZM$ , each being half of the given angle.