EMAT 6700
by Brad Simmons
Constructing a Decagon
Use geometer's sketchpad to construct a decagon.
1. Construct circle O of radius 1 unit, tangent to a line at point A.
2. Mark off 2 unit from point A to locate point P on the line.
3. Construct segment OP and label point Q where the segment intersects the circle.
(By the Pythagorean Theorem, segment OP = the square root of 5. Segment PQ = (the square root of 5) minus 1.)
4. Bisect segment PQ and label the midpoint as R.
(The segment PR has a length ((the square root of 5) minus 1) divided by 2.)
5. Select segment PR and point A. Construct circle by center and radius.
6. Use a radius of the length of segment PR to mark 10 points around the circle.
7. Connect the 10 point to form a decagon.
8. Hide the construction objects.
Please click here for a geometer's sketchpad sketch of the figure shown above.
What is the measure of angle AOB?
What is the measure of segment AB?
What is the measure of segment AB if left in radical form?
Please click here for a geometer's sketchpad sketch of the figure shown above.