Construct An Angle Bisector

An angle bisector is a straight line that divides the angle into two equal parts.

Example : Construct an angle bisector for the following angle:

Solution:

Step 1 : Put the sharp end of your compasses at point B and make one arc on the line BC (point S) and another arc on line AB (point T).

Step 2 : Without changing the width of your compasses, put the sharp end of the compasses at S and make an arc within the lines AB and BC. Do the same at T and make sure that the second arc intersects the first arc.

Step 3 : Draw a line from point B to the points of intersection of the 2 arcs. This line bisects .

The following video shows how to draw an angle bisector

The following video shows how to bisect a given angle using only a compass and straightedge.

We can use the angle bisector to construct some other angles from existing angles.

Example :

A 30˚ angle can be obtained by bisecting a 60˚ angle.

A 15˚ angle can be obtained by bisecting a 30˚ angle.

A 45˚ angle can be obtained by bisecting a 90˚ angle.

A 22.5˚ angle can be obtained by bisecting a 45˚ angle.

Example:

The figure shows a point A on a straight line. Construct an angle of 45˚ at point A.

Solution:

Construct a 90˚ angle, and then construct an angle bisector to obtain a 45˚ angle.

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