Question

a perpendicular bisector of a segment is a line, segment, or ray that is perpendicular to the segment at its midpoint. 9. circle the drawing that shows the perpendicular bisector of a segment. problem 3 constructing the perpendicular bisector got it? draw $overline{st}$. construct its perpendicular bisector. 10. error analysis a students construction of the perpendicular bisector of $overline{st}$ is shown below. describe the students error. 11. do the construction correctly in the box below.

Explanation:

Step1: Recall perpendicular - bisector definition

A perpendicular bisector of a segment is perpendicular to the segment and passes through its mid - point.

Step2: Analyze student's construction error

The student's construction is incorrect because the arcs drawn from points \(S\) and \(T\) to construct the perpendicular bisector seem to be of unequal radii. When constructing a perpendicular bisector, we use a compass to draw arcs of equal radii from both endpoints of the segment.

Step3: Correct construction steps

1. Place the compass at point \(S\) and set the width of the compass to a length greater than half of the length of \(\overline{ST}\).
2. Draw arcs above and below the segment \(\overline{ST}\).
3. Without changing the compass width, place the compass at point \(T\) and draw arcs above and below the segment \(\overline{ST}\) that intersect the previously drawn arcs.
4. Draw a line through the intersection points of the arcs. This line is the perpendicular bisector of \(\overline{ST}\).

Answer:

The student's error is that the arcs drawn from \(S\) and \(T\) to construct the perpendicular bisector are of unequal radii. The correct construction involves drawing arcs of equal radii from both \(S\) and \(T\) and then connecting the intersection points of the arcs to form the perpendicular bisector.