Question

Draw a line $\overrightarrow{\mathit{A}\mathit{B}}$. Choose a point $\mathit{O}$between $\mathit{A}$and $\mathit{B}$. Use a protractor to investigate the following questions.

In the plane represented by your paper, how, many lines can you draw through $\mathit{O}$that will form a $\mathbf{90}\mathbf{°}$angle with $\overrightarrow{\mathit{O}\mathit{B}}$?

Short answer

Maximum 2 lines can be drawn.

Step-by-step solution

- Apply the protractor postulate

$\overline{\mathit{A}\mathit{H}}$in a given plane is considered.

Any point $\mathit{O}$between $\mathit{A}$and $\mathit{H}$is chosen.

Consider role="math" localid="1649228271615" $\overline{\mathit{O}\mathit{A}}$and $\overline{\mathit{O}\mathit{H}}$all these rays are drawn from $\mathit{O}$on one side of role="math" localid="1649228317831" $\overline{\mathit{A}\mathit{H}}$.

These rays’ results in pairing with the real numbers from 0 to 180 in such a way that:

The line $\overline{\mathit{O}\mathit{A}}$is paired with 0, and $\overline{\mathit{O}\mathit{H}}$with 180.

If $\overline{\mathit{O}\mathit{B}}$is paired with $\mathit{x}$, and $\overline{\mathit{O}\mathit{C}}$with $\mathit{y}$, then $\mathit{m}\mathit{\angle }\mathit{B}\mathit{O}\mathit{C}\mathit{=}\left|x-y\right|$.

- Sketch the figure

Thus, the figure is shown below, such that four lines are drawn through $O$that will form a $90°$angle.

- Observation of the figure

As it can be seen from the above figure, that on the plane of the paper through point $O$between $A$and $B$, there are maximum two lines that will make $90°$with $\overline{OB}$.

The line $\overline{OC}$can be drawn using protractor on one side of the $\overline{AB}$and $\overline{OD}$on the other side of the $\overline{AB}$.

Therefore, only 2 lines can be drawn through point $O$to form $90°$with $\overline{OB}$.