Chapter 1.4, Problem 27CE

To determine

To examine: How the angle $\angle \text{AOB}$ related to $\overline{OK}$ .

Answer to Problem 27CE

  $\overline{\text{OK}}\text{acts}\text{as}\text{bisector}\text{of}\angle \text{AOB}$

Explanation of Solution

Given information:

Draw an angle. $\angle \text{AOB}$ on a sheet of paper. Fold the paper so that $\overline{OA}$ vector falls on $\overline{OB}$ . Lay the paper flat and call the fold line $\overline{OK}$ .

Formula used:

Congruent angles

Calculation:

Considering the Statement of the problem:

The figure can be drawn as shown below,

  

From the above figure it can be observe that after folding $\angle AOB$ line $\overline{OA}$ a falls on $\overline{OB}$ . And the folding line is named as $\overline{OK}$ shown in the above figure.

Further it can be seen in figure that $\overline{OK}$ divides $\angle AOB$ into two congruent angles that means;

  $\angle \text{AOK}=\angle \text{BOK}$

Therefore,

  $\overline{\text{OK}}\text{acts}\text{as}\text{bisector}\text{of}\angle \text{AOB}$

Conclusion:

  $\overline{\text{OK}}\text{acts}\text{as}\text{the bisector}\text{of}\angle \text{AOB}$