Lesson 1 Under Construction Develop Understanding

Ready

1.

Using your compass, construct several concentric circles that have point $A$ as a center and a radius larger than $\frac{1}{2}$ the length of segment $A B$ . Each time you construct a circle with a center at $A$ , construct a congruent circle with a center at point $B$ . What do you notice about where all the circles with center $A$ intersect with all the corresponding circles with center $B$ ?

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.

b.

c.

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 $D E$ . Label the image $D^{'} E^{'}$ .

7.

Use a compass and a straightedge to copy the angle.

8.

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

9.

Construct a square using segment $C D$ as a side of the square and points $D$ and $C$ 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.

11.

${\begin{cases} x = 11 + y \\ 2 x + y = 19 \end{cases}$

12.

${\begin{cases} - 4 x + 9 y = 9 \\ x - 3 y = - 6 \end{cases}$

13.

${\begin{cases} x + 2 y = 11 \\ x - 4 y = 2 \end{cases}$

14.

${\begin{cases} y = - x + 1 \\ y = 2 x + 1 \end{cases}$

15.

${\begin{cases} y = - 2 x + 7 \\ - 3 x + y = - 8 \end{cases}$

16.

${\begin{cases} 4 x - y = 7 \\ - 6 x + 2 y = 8 \end{cases}$