Using your compass, 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]?
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.
For each regular polygon, use your compass to construct a circle with the same center as the polygon and through all the vertices of the polygon.
For each regular polygon, use your compass to construct a circle with the same center as the polygon and through all the vertices of the polygon.
For each regular polygon, use your compass to construct a circle with the same center as the polygon and through all the vertices of the polygon.
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.
Use a compass and a straightedge to bisect the angle. Check your construction by folding the paper.
Use a compass and a straightedge to copy segment [math]DE[/math].
Use a compass and a straightedge to copy the angle.
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.
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.
Use a compass and a straightedge to locate the center of rotational symmetry of the equilateral triangle.
[math]x=11+y[/math][br][math]2x+y=19[/math]
[math]-4x+9y=9[/math][br][math]x-3y=-6[/math]
[math]x+2y=11[/math][br][math]x-4y=2[/math]
[math]y=-x+1[/math][br][math]y=2x+1[/math]
[math]y=-2x+7[/math][br][math]-3x+y=-8[/math]
[math]4x-y=7[/math][br][math]-6x+2y=8[/math]