Chapter 10.5, Problem 18WE

To determine

To show: that the student did not trisect $\angle G$ .

Explanation of Solution

Given Information:

To trisect a general angle $G$ , a student tried this procedure:

1. Mark off $\overline{GA}$ congruent to $\overline{GB}$ .
2. Draw $\overline{AB}$ .
3. Divide $\overline{AB}$ into three congruent parts.
4. Draw $\overline{GX}$ and $\overline{GY}$

Given figure,

  

Calculation:

Draw an arc $AB$ taking $\overline{GB}$ as radius and $G$ as center.

It clearly shows $\overline{GA}>\overline{GY}$

Assume $\angle 1=\angle 2$ therefore, $\overline{GX}$ is angle bisector of $\angle AGY$ .

Use angle bisector theorem:

  $\frac{GA}{GY}=\frac{XA}{XY}$

But, here seen $\overline{GA}>\overline{GY}$ and it is known $XA=XY$ .

Hence, $\frac{GA}{GY}\ne \frac{XA}{XY}$ and therefore, $\angle 1\ne \angle 2$ .