Constructing a 30-degree Angle
We will also need to know
how to construct an angle having a measure of 30°. We know that each interior angle of an equilateral triangle is 60°, so we can do a construction similar to the
construction of an equilateral triangle and then bisect one of the angles. First, construct the segment j between A and
B. Construct the circle c1
centered at A through the point B.
Construct the circle c2 centered at B through the point
A. Construct one of the points of
intersection of the two circles, and label it C. Construct segments AC and BC.
Then ABC is an equilateral triangle, so the measure of angle CAB is 60°.
Construct the bisector m of angle CAB.
Construct the intersection D of line m and segment CB. The measure of angle DAB is 30°.
Click here for a script to construct an angle DAB having a measure of 30° given points A and B.
Click here for a GSP sketch of the
construction.
