Question

Anton will be constructing a segment bisector with a compass and straightedge, while Maxim will be constructing an angle bisector with a compass and straightedge. Describe the similarities and differences between their construction steps.

Answer 1

A bisector is a line that divides either a line or an angle into two proportionate parts or angles. Thus, Anton's bisector would divide the segment into two equal parts, while Maxim's bisector would divide the angle into two equal angles.

The similarities between their construction are:

• Intersecting arcs through which the bisector would pass are required.
• The arcs are dawn using the same radius of any measure.
• The edges of the arc of the given angle, and the ends of the segment are used as centers.

The differences between their construction are:

• Anton has to draw two intersecting arcs above and below the segment. While Maxim would draw two intersecting arcs within the lines forming the angles.
• Anton's bisector would be perpendicular to the segment, while Maxim's bisector would be at an angle which is half of the initial angle.

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