Question

Select the correct answer from each drop-down menu. The given diagram shows a construction completed using a straightedge and a compass. What is the construction shown in the diagram?

1) Bisecting an angle
2) Constructing a perpendicular bisector
3) Constructing an equilateral triangle
4) Constructing a parallel line

Answer 1

Constructing a perpendicular bisector

Step-by-step explanation:

The construction depicted in the diagram involves creating a perpendicular bisector. This geometric construction method employs a straightedge and compass to establish a line that is both perpendicular to another line and bisects it, dividing it into two equal parts.

The process begins with the selection of two points on the given line segment. Using the compass, circles are drawn centered at each of these points, and the intersection points of these circles determine the mid-point of the line segment. The straightedge is then employed to draw a line passing through this mid-point and perpendicular to the original line, thereby constructing the perpendicular bisector.

This construction is particularly useful in geometry and various applications where a perpendicular bisector is needed, such as in the creation of regular polygons or the identification of the center of a circle circumscribed around a triangle. The method's precision relies on the careful use of the compass and straightedge to ensure accurate construction in accordance with geometric principles.