Subjects
Grades
Constructing a Bisector
Concept sheet | Mathematics
Secondary
1-2
Table of contents
The bisector is a line (or line segment) that divides an angle into two equal angles.
A bisector can be considered the axis of symmetry of an angle. Thus, each point belonging to a bisector is located the same distance from the two sides that make up the angle.
We can draw the bisector of an angle in two ways:
We can construct the bisector of an angle, whether it is included in a plane figure or not.
Compass and Ruler Method
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Open the compass and keep the same opening for all steps of the construction.
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Place the compass’ sharp point on the angle’s apex (vertex) and draw an arc that intersects both sides of the angle.
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Place the compass’ sharp point on an intersection of the circle’s arc and one side of the angle. Draw a new arc in the angle opening. Repeat the operation from the other intersection point.
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Using a ruler, draw the straight line that connects the angle’s vertex to the intersection point of the last two drawn arcs. This straight line is the bisector of the angle.
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Open the compass and keep the same opening for all steps of the construction.
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Place the compass’ sharp point on the angle’s apex (vertex) and draw an arc that intersects both sides of the angle.
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Place the compass’ sharp point at an intersection of the circle’s arc and one side of the angle. Draw a new arc in the angle opening. Repeat the operation from the other intersection point.
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Using a ruler, draw the straight line that connects the angle’s vertex to the intersection point of the last two arcs drawn. This line is the angle’s bisector.
Protractor Method
You can use a protractor to draw the bisector of an angle by following these steps:
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With a protractor, measure the angle you want to separate into two equal parts.
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Divide the angle value in half.
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Trace the angle calculated in step 2 using the protractor and a ruler.
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Using a protractor, measure the angle you want to separate into two equal parts.
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Divide the angle’s value in half.
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Draw the angle calculated in step 2 using the protractor and a ruler.
