Question

Ben uses a compass and a straightedge to bisect angle PQR, as shown below:

Answer 1

GIVEN:

We are given a diagram depicting the process of bisecting an angle.

The angle being bisected is angle PQR, and the point at which it is bisected is labeled point S which gives rise to angle PQT and angle TQR.

Required;

To select which of the given statements best explains why the same width is used to draw arcs from A and B that intersect at S.

Explanation;

To bisect the angle, a compass is used to draw an arc from A to point S. Along the same arc on line QR the compass is also used to draw another arc from B also to point S. Note that the width of the compass must not be altered at the point of drawing the second arc from point B.

This means the distance AS equals BS. Also, AQ equals BQ.

Therefore at the point S, we can easily conclude that the angle formed by AQS is the same as that formed by BQS.

Therefore,

ANSWER:

`\begin{gathered} \angle AQS\cong\angle BQS \\ \\ When\text{ }AS=BS\text{ }and\text{ }AQ=BQ \end{gathered}`

The third option is the correct answer.