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 st. construct its perpendicular bisector. 10. error analysis: a students construction of the perpendicular bisector of st is shown below. describe the students error. 11. do the construction correctly in the box below.

Explanation:

Step1: Recall perpendicular - bisector construction

A perpendicular bisector of a line segment \(ST\) is a line that is perpendicular to \(ST\) and passes through its mid - point. The correct construction involves using a compass to draw arcs of equal radius from both endpoints \(S\) and \(T\).

Step2: Analyze the student's error

The student likely did not use equal radii when drawing the arcs from points \(S\) and \(T\). To construct the perpendicular bisector, we need to set the compass width to a length greater than half of the length of \(ST\) and draw arcs from both \(S\) and \(T\). The intersection points of these arcs are then used to draw the perpendicular bisector.

Step3: Correct construction steps

1. Open the compass to a width greater than \(\frac{1}{2}ST\).
2. Place the compass at point \(S\) and draw an arc above and below the line segment \(ST\).
3. Without changing the compass width, place the compass at point \(T\) and draw an arc above and below the line segment \(ST\). These arcs will intersect the previous arcs at two points.
4. Use a straight - edge to draw a line through the two intersection points of the arcs. This line is the perpendicular bisector of \(ST\).

Answer:

The student likely did not use equal radii for the arcs drawn from \(S\) and \(T\). The correct construction involves using a compass to draw arcs of equal radius from both \(S\) and \(T\) and then drawing a line through the intersection points of the arcs to get the perpendicular bisector of \(ST\).