Question

1. Use a compass to draw a large circle.

2. Without changing the compass setting, place the point of the compass on the circle and make a mark that intersects the circle.

3. Move the point of the compass to the mark you made and make another mark that intersects the circle.

4. Continue in this way around the circle until you come back to the first mark.

(Hint: The last mark might not coincide precisely with the first mark, but your drawing should look something like the sketch.)

5. Select one of the marks on the circle and use a straightedge to draw line segments connecting that mark to all the marks that are not next to it.

6. Repeat the process for each mark on the circle.

With the design you created in the previous question. Select a pair of adjacent compass marks on the circle. Then follow these instructions and answer the question. 1. Make a crease by folding the paper so that the two marks coincide with each other. When you open the paper, the crease will show you the midpoint along the circle between the two marks. 2. Repeat the process to find the midpoint between each pair of marks on the circle. 3. Use a straightedge to draw line segments connecting each midpoint to the midpoint that is next to it. What type of figure did you create?

Answer 1

So, the first shape is a pentagon, and the second figure, the one asked for, is a decagon (ten sided polygon), because each 'midpoint line' had two ends, which were factored in and doubled the amount of sides.