# Lesson 1 Equilateral Triangle

Joe and Marty are in the park playing catch. Tony joins them, and the boys want to stand so that the distance between any two of them is the same. Where do they stand? How do they figure this out precisely? What tool or tools could they use?

Write the definitions of segment, radius, and circle.

Margie has three cats. She has heard that cats in a room position themselves at equal distances from one another and wants to test that theory. Margie notices that Simon, her tabby cat, is in the center of her bed (at S), while JoJo, her Siamese, is lying on her desk chair (at J). If the theory is true, where will she find Mack, her Calico cat? Use the scale drawing of Margie's room shown below, together with (only) a compass and straightedge. Place an M where Mack will be if the theory is true.

## Construct an equilateral triangle using the steps below.

1. Draw segment AB.
2. Draw circle A with radius AB.
3. Draw circle B with radius BA.
4. Label an intersection of circle A and circle B as C.
5. Draw segment CA and segment CB.

## Challenge #1

Using the skills you have practiced, construct three equilateral triangles, where the first and second triangles share a common side and the second and third triangles share a common side.

## Challenge #2

Use the skills you have developed in this lesson to construct a regular hexagon.