NAME:
Chapter 6 Activities:
The Four Point Geometry
12 points
SAME
07 points
DIFFERENT
07 points
Saccheri Quadrilaterals
12 points
1
The Four Point Geometry
Undefined terms
Axioms
point, line, on
A1
There are exactly four points.
A2
Any two distinct points have exactly one line on both of them.
A3
Each line is on exactly two points.
Models – categorical
Possible Definitions:
Parallel lines
Collinear points
Theorems
1. The four point geometry has exactly 6 lines.
2. Each point of the geometry has exactly 3 lines on it.
2
Discuss ways that this is similar to and different from Euclidean Geometry. Have at least 5 of
each.
3
List 7 things that are the SAME in Hyperbolic, Euclidean, and Spherical?
4
List 7 things that are DIFFERENT between Hyperbolic, Euclidean, and Spherical?
5
Saccheri Quadrilaterals
Definition:
Picture:
Fill in the following chart
Geometry
Summit angles type
(acute, right, obtuse)
Summit to base
comparison (<, >, =)
Euclidean
Spherical
Hyperbolic
6