Lesson 1 Under Construction Develop Understanding

Ready

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 ?

Line segment AB

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.

a.

Regular hexagon with center point

b.

Regular octagon with center point

c.

Regular decagon with center point

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.

Angle B composed of line segment BA and line segment BC

6.

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

Line segment DE

7.

Use a compass and a straightedge to copy the angle.

an 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.

Line segment AB

9.

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

Line segment DC

10.

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

equilateral triangle

Go

Solve each system of equations.

11.

12.

13.

14.

15.

16.