Q27 - Geometry

Question

Draw an angle, $\angle AOB$, on a sheet of paper. Fold the paper so that $\overline{OA}$ falls on $\overline{OB}$. Lay the paper flat and call the fold line $\overline{OK}$. How is $\overline{OK}$ related to $\angle AOB$? Explain.

Step-by-Step Solution

Answer

$\overline{\mathbf{O}\mathbf{K}}$ acts as a bisector of $\mathbf{\angle }\mathit{A}\mathit{O}\mathit{B}$.

Step 1. Draw a diagram.

Draw a diagram based on the given instructions.

Step 2. Description of step.

From the figure it can be observed that after folding $\angle AOB$, line $\overline{OA}$ falls on $\overline{OB}$ and the line folding line is named as $\overline{OK}$.

Step 3. Description of step.

From the figure it can be observed that $\overline{OK}$ divides $\angle AOB$ into two congruent angles that means; $\angle AOK=\angle BOK$. Therefore, $\overline{OK}$ acts as a bisector of $\angle AOB$.

 

Therefore, $\overline{OK}$ acts as a bisector of $\angle AOB$.