- In the PoincarŽ model, follow Euclid's proof of proposition 1 to construct an equilateral triangle ABC.
- Draw line segment AB
- Draw circle with center A and radius AB
- Draw circle with center B and radius BA
- Construct the points of intersection C, D
- Draw line segments, AC, BC

- Measure triangle ABC
- Move points A and B around the space and answer the following questions:
- Are the sides of your triangle always equal?
- Are the angles of your triangle always equal?
- What is the largest angle sum possible? What does the triangle look like when you get close to this sum?
- What is the smallest angle sum possible? What does the triangle look like when you get close to this sum?

- Change to the half plane model of hyperbolic geometry and repeat steps 1, 2, 3.

Last Update: October 4, 2006

Ronald K. Smith

Graceland University

Lamoni, IA 50140

rsmith@graceland.edu Modern Geometry Fall 2006