´╗┐Objective(s)

  • Create diagrams using a straightedge
  • Use a compass to construct a circle

Required materials: compass, straightedge, patty paper


Warm Up

Gain familiarity with the construction tools by drawing multiple lines and circles. Then, follow these steps:

  • Draw a point, label it
  • Draw a circle centered at
  • Mark a point on the circle, label it
  • Draw a circle centered at going through
  • Draw segment

Definitions

Line segment: a set of points on a line with two endpoints

Circle: a set of all points that are the same distance (radius) from a given point (center)


Illegal Moves

Given segment , follow these steps:

  • Draw a circle centered at with radius
  • Mark a point at the middle of , label it
  • Draw a circle centered at with radius
  • Label the intersection above as and below as
  • Draw segments , , and , and trace onto patty paper

Discussion

Compare your with your neighbors.

Why might they be different? How could we ensure they are all the same?


Valid Construction Moves

  • Draw points in blank space, on objects, and at intersections
  • Draw segments, rays, and lines through two points
  • Draw a circle centered at a point and through another point
  • Set compass to a length between two points then move the compass

Perfect Copy

The figure shows the first few steps of constructing a regular hexagon. Complete the construction.

(image)


Reflection

How does your regular hexagon compare to your neighbors?

A regular polygon has sides with equal lengths. How can you be sure your hexagon is a regular hexagon?


Summary

A straightedge can be used to create line segments. Line segments are named by its endpoints.

A compass can be used to create circles. Circles are named by its center and radius.