1. Using Geogebra tools, construct several concentric circles that have point [math]A[/math] as a center and a radius larger than [math]\frac{1}{2}[/math] the length of segment [math]AB[/math]. Each time you construct a circle with a center at [math]A[/math], construct a congruent circle with a center at point [math]B[/math]. What do you notice about where all the circles with center [math]A[/math] intersect with all the corresponding circles with center [math]B[/math]?
2. In the first problem, you have demonstrated one way to find the midpoint of a line segment. Explain another way a line segment can be bisected without the use of circles.
3. For the regular polygon below, construct a circle with the same center as the polygon and through all the vertices of the polygon.
4. For the regular polygon below, construct a circle with the same center as the polygon and through all the vertices of the polygon.
5. For the regular polygon below, construct a circle with the same center as the polygon and through all the vertices of the polygon.
6. The tools of geometric construction are a compass and a straightedge. A compass will make circles, while a straightedge helps in making straight lines. Explain why circles are so useful in making geometric constructions.
7. Use Geogebra tools to bisect the angle. Check your construction by labeling the angles.
8. Use Geogebra tools to copy segment [math]DE[/math].
9. Use Geogebra tools to copy the angle.
10. Construct a rhombus using segment [math]AB[/math] as a side and points [math]A[/math] and [math]B[/math] as two of the vertices of the rhombus. Let angle [math]A[/math] be one of the angles of the rhombus.
11. Construct a square using segment [math]CD[/math] as a side of the square and points [math]C[/math] and [math]D[/math] as two of the vertices of the square.
12. Use Geogebra tools to locate the center of rotational symmetry of the equilateral triangle.