A bisector is the required line that divides a given line or an angle into two equal parts. The required construction of the bisectors is shown in the attachment to this answer.
Bisection is the process in which a given line or angle is divided into two equal parts by constructing the required bisector. Thus the steps to bisect the given arcs are stated below:
For figure 1:
- Open the compass to any radius, using point A as the center draw arcs on the reverse side of the given arc AB.
- Repeat the same process using point B as the center and the same radius as that used in A.
- Join the intersections of the arcs on the reverse sides of arc AB by a line. Thus the required bisector.
For figure 2:
- Open the compass to any radius, using point M as the center draw arcs on the reverse side of the given arc MN.
- Repeat the same process using point N as the center and the same radius as that used in M.
- Join the intersections of the arcs on the reverse sides of arc MN by a line. Thus the required bisector.
For figure 3:
- Open the compass to any radius, using point A as the center draw arcs on the reverse side of the given arc AB.
- Repeat the same process using point B as the center and the same radius as that used in A.
- Join the intersections of the arcs on the reverse sides of arc AB by a line. Thus the required bisector.
- The point on arc AB through which the bisector intersects is the required point S. The mid point of arc AB.
For figure 4:
- Open the compass to any radius, using point A as the center draw arcs on the reverse side of the given arc AB.
- Repeat the same process using point B as the center and the same radius as that used in A.
- Join the intersections of the arcs on the reverse sides of arc AB by a line. Thus the required bisector.
- Repeat the same procedures using points BC.
NB: The point of intersection of the bisectors in relation to arc AC is the radius of the given arc.
The required constructions are attached to this answer.
For more clarifications on the bisection of arcs, visit: https://brainly.com/question/1846300
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