How do you draw a perpendicular bisector?
Drawing perpendicular bisector for a line: Place the sharp end of a pair of compasses at one end of the line, and open it to just over half of the line. Draw an arc which must intersect the line in the position described. Then put the sharp end at the other of the line and, keeping the compassing at the same length, draw another arc which intersects the first one twice and also the line. Then draw a straight line through the two places where the arcs intersect. This line is the perpendicular bisector.
Drawing perpendicular bisector of angle: Places the sharp end of the compass at the point of the angle and, after having opened it arbitraily wide, draw an arc which intersects the two lines meeting to form the angle each once in the said position. Then remove the compass and, always keeping it opened at the SAME length, place the sharp end at each of the two places where the previous arc cuts each of the two lines meeting to form the angle. In this position with the described length, draw a small arc at each of the said places, which should cross each other. Draw a straight line from the point of the angle to this crossing. This should be the bisector of the angle.
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When constructing an angle bisector, why must the arcs intersect?
The arcs must intersect in order to connect to the vertex of the angle.
When constructing an angle bisector, we open our compass to any width, and place the point of the compass on the vertex of the angle. We then construct an arc through both sides of the angle.
Next we move the compass to the point where our constructed arc intersects one side of the angle. We then draw an arc inside of the angle.
Using the compass set to the same width, we move the compass to the point where our first arc intersects the other side of the angle, drawing an arc inside of the angle. This new arc will intersect our previous arc, creating a point.
We then use a straightedge to connect this point to the vertex of the angle, giving us our bisector.
If the two arcs did not intersect, we would not have a point to connect to the vertex.
A perpendicular bisector is a line that bisects a line segment in two equal parts and makes an angle of 90 degrees at the point of intersection. In other words, we can say that a perpendicular bisector divides a line segment at its midpoint making an angle of 90 degrees. Let us go through the formal definition of it in the next section to understand its meaning in a better way.
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A perpendicular bisector is defined as a line or a line segment that divides a given line segment into two parts of equal measurement. ‘Bisect’ is the term used to describe dividing equally. Perpendicular bisectors intersect the line segment that they bisect and make four angles of 90° each on both sides. Perpendicular means a line or a line segment making an angle of 90° with another line or line segment. In the figure shown below, the perpendicular bisector bisects the line segment AB into two equal halves.
Follow the steps below to construct a perpendicular bisector of a line segment.
Perpendicular bisectors can bisect a line segment or a line or the sides of a triangle. The important properties of a perpendicular bisector are listed below.
Important Notes on Perpendicular Bisector
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FAQ
How is constructing an angle bisector?
What do you need to prove a line is an angle bisector of an angle?
