Compass and a straight edge required for both construction
Both construction includes a line drawn from the intersection of arcs to bisect a segment or an angle
The bases for the construction of both bisector are the ends of segment and the angle to be bisected
The width of the compass when drawing intersecting arcs, is more than half the width of the segment or angle being bisected
The differences are;
Two points of intersection of arcs are used in the segment bisector while only one is requited in an angle bisector
The bisecting line crosses the segment in a segment bisector, while it stops at the vertex of the angle being bisected in an angle bisector
The sources of the above equations are as follows;
The steps to construct a segment bisector are;
Place the needle of the compass at one of the ends of the line segment to be bisected
Widen the compass so as to extend more than half of the length of the segment to be bisected
Draw two arcs, one above, and the other below the line
Place the compass needle at the other end and with the same compass width draw arcs that intersects with the arcs drawn in the above step
Draw a line segment by placing the ruler on the points of intersection of the arcs above and below the line
The steps to construct an angle bisector are;
With the compass needle at the vertex, open the pencil end such that arcs can be drawn on the rays (lines) forming the angle
Draw an arc on both lines forming the angle
Place the compass needle at one of the intersection points and draw an arc in between the lines forming the angle
Repeat the above step with the same compass width from the other intersection point with the rays forming the angle
Join the point of intersection of the two arcs to the vertex of the angle to bisect the angle
Therefore, we have;
The similarities are;
A compass and a straight edge can be used for both construction
A straight line is drawn from the point of intersection of arcs to bisect the segment or the angle
The arcs are drawn from the ends of the segment or angle to be bisected
The width of the compass is more than half the width of the line or angle when drawing the arcs
The differences are;
In a segment bisector, the intersection point is above and below the line, while in an angle bisector only one pair of arcs are drawn to intersect above the line
The bisecting line passes through the segment being bisected, while the line stops at the vertex in an angle bisector
Learn more about the construction of segment and angle bisectors here;
