Question

multiple choice 5 points
which diagram shows the construction of a perpendicular bisector?

1. diagram with two intersecting ovals and a line ab and a perpendicular line
2. diagram with a semicircle and a line ab and a perpendicular line
3. diagram with two intersecting arcs and a line ab and a perpendicular line
4. diagram with two intersecting arcs above and a semicircle below, and a line ab and a perpendicular line

options: 2, 4, 1, 3

Explanation:

Step1: Recall Perpendicular Bisector Construction

To construct a perpendicular bisector of a segment \( AB \), we draw two arcs with the same radius, one centered at \( A \) and one at \( B \), intersecting above and below the segment. Then, the line through these intersection points is the perpendicular bisector.

Step2: Analyze Each Diagram

• Diagram 1: Has two pairs of arcs (above and below \( AB \)) intersecting, forming a line that is perpendicular to \( AB \) and bisects it (since the arcs are symmetric around \( AB \)'s midpoint).
• Diagram 2: Only one arc, not the standard construction.
• Diagram 3: Arcs are symmetric but the construction doesn't match the perpendicular bisector steps (arcs are on the sides, not above and below with two intersections).
• Diagram 4: Arcs are not symmetric or following the standard perpendicular bisector construction.

Answer:

1. The diagram labeled 1 (with two pairs of intersecting arcs above and below segment \( AB \), forming a perpendicular line through \( AB \)'s midpoint)