## ﻿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 $A$
• Draw a circle centered at $A$
• Mark a point on the circle, label it $B$
• Draw a circle centered at $B$ going through $A$
• Draw segment $\overline{AB}$

### 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 $\overline{AB}$, follow these steps:

• Draw a circle centered at $A$ with radius $AB$
• Mark a point at the middle of $\overline{AB}$, label it $C$
• Draw a circle centered at $B$ with radius $BC$
• Label the intersection above $B$ as $D$ and below $B$ as $E$
• Draw segments $\overline{AD}$, $\overline{DE}$, and $\overline{AE}$, and trace $\Delta ADE$ onto patty paper

### Discussion

Compare your $\Delta ADE$ 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.