Lesson 1Under ConstructionDevelop Understanding

1.

Using your compass, construct several concentric circles that have point as a center and a radius larger than the length of segment . Each time you construct a circle with a center at , construct a congruent circle with a center at point . What do you notice about where all the circles with center intersect with all the corresponding circles with center ?

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 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.

Set

4.

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.

5.

Use a compass and a straightedge to bisect the angle. Check your construction by folding the paper.

6.

Use a compass and a straightedge to copy segment . Label the image .

7.

Use a compass and a straightedge to copy the angle.

8.

Construct a rhombus using segment as a side and points and as two of the vertices of the rhombus. Let angle be one of the angles of the rhombus.

9.

Construct a square using segment as a side of the square and points and as two of the vertices of the square.

10.

Use a compass and a straightedge to locate the center of rotational symmetry of the equilateral triangle.

Go

Solve each system of equations.