Example: Construct an angle bisector for the following angle:
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 : 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 ∠ABC.
The steps to construct an angle bisector can be summarized as follows:
1. From the vertex, draw an arc across both rays of the angle.
2. From each arc intersection draw another pair of arcs that intersect each other.
3. Draw a line from the vertex to the intersection point to form the angle bisector.
We can use the angle bisector to construct some other angles from existing angles.
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.
The figure shows a point A on a straight line. Construct an angle of 45˚ at point A.
Construct a 90˚ angle, and then construct an angle bisector to obtain a 45˚ angle.
How to construct 30, 45, 60, 90, and 120 degree angles with a compass by constructing angle bisectors?
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