Chapter 6 Activities
NAME:
A Flexible Geometry
10 points
The 3 Point Geometry
10 points
The 5 Point Geometry
10 points
Incidence Geometry
10 points
Taxicab Geometry
10 points
Taxicab 3 – 4
10 points
Saccheri Quadrilaterals
10 points
The List
10 points
A Flexible Geometry
Are there a minimum number of points?
Is there a relationship between the number of points and the number of lines?
What might be a good model different from the two presented? (10 minutes!)
The Three point Geometry
Prove this theorem:
Theorem 2:
There are exactly 3 distinct lines in this geometry.
Suppose there are FOUR lines in this geometry…
The Five Point Geometry
5 Point Geometry Exercise:
How many pairs of parallel lines are there?
P1
Points: {P1, P2, P3, P4, P5}
P2
P5
Lines: {P1P2, P1P3, P1P4, P1P5, P2P3, P2P4, P2P5,
P3
P4
P3P4, P3P5, P4P5}
An Incidence Geomtry
Finite point model
Find at least two ways that this geometry is like Euclidean Geometry.
Find three ways that this geometry is different from Euclidean Geometry.
Taxicab Geometry
What’s the connection between the slope and the Geometric Taxicab Coordinate?
Taxicab Geometry
Put a right triangle with leg lengths 3 and 4 in Quadrant 1
What is the measure of the hypotenuse?
What are the measures of the angles? How will you find them using a calculator?
Saccheri Quadrilaterals
Why do we care?
Make a list of things that are the same and different with EG, SG, and HG