The objective of this section is to have the students understand how to use a compass and straightedge for construction. I think it is also important for the students to understand how to do the same constructions with software...since these are the tools of today and the future.
Therefore with Geometry Sketchpad we can also demonstrate example number three, then have the students construct a six-pointed star. There is a couple of ways to accomplish this...
1. You can have to students explore with the Sketchpad and challenge to see if they can accomplish it with no real direction.
2. You can provide them step by step intructions to help guide their understanding, either with the specific guidance in parenthesis or just general direction.
Since we are not using a compass, we have to approach the construction from a different angle. We need to be able to construct arches around the circle which equal the measure of the radius. So how do we approach this with Sketchpad?
a. One way would be to construct a line segment; after selecting the line segment you want to find the midpoint. (We do this from the "Construct" menu; select "Midpoint".)
b. From here we need to construct a circle to work with so selecting the midpoint as the center and one of the endpoints of the segment as another point we construct our circle. (Select the midpoint first then an endpoint; from the "Construct" menu, select "Circle by Center + Point")
c. Now we need to construct arcs on the circle equidistant to the measure of the radius. To do this we can construct two more circlesthis time using the endpoints of the line segment as the center and the midpoint as the point to lie on the circle. (Select one endpoint then select the midpoint; From the "Construct" menu, select "Circle by Center + Point"; then repeat using the other endpoint.)
d. If we mark the points where the three circles intercept, these points would be equidistant to the measure of the radius.
e. To then see what we are working with we need to focus on the main circle with the six points we have identified on the original circle. Our points on the circle are the four points from the intersection of the circles and two points which were the endpoints of our line segment. (Select the two outside circles, the line segment, and the midpoint; From the "Display" menu; Select "Hide Objects")
f. To finish our six-sided figure we just need to construct line segments between our points around the circle. (Select the points around the circle, in order; From the "Construct" menu, Select "Segments"