November 25

The NonEuclid Simulation with Congruence and Polygons

Euclidean Geometry has both similar and congruent polygons. All congruent polygons are similar, but the reverse is not true. What is the relationship between similarity and congruent in hyperbolic geometry?

Run NonEuclid Applet (click button below):

Required Exercises:

Activities: Adjacent Angles, Angles, Parallel Lines, General Triangles,
Isosceles Triangles, Equilateral Triangle, Right Triangles, Congruent Triangles,
Rectangles & Squares, Parallelograms, Rhombus, Polygons, Circles, Tessellations of the Plane.

More Concepts:

Axioms and Theorems: - Euclid's Postulates, Hyperbolic Parallel Postulate,
SAS Postulate, Hyperbolic Geometry Proofs.

Area: - A=1/2bh, Altitudes of a Hyperbolic Triangle, Defect of a Triangle, Defect of a Polygon,
Properties Necessary for an Area Function, Upper Bound to Area.

X-Y Coordinate System -  A description of how an x-y coordinate system
can be set up in Hyperbolic Geometry.

Disk and Upper Half-Plane Models: - A semiformal development of each model.

For The Teacher: Why is it Important for Students to Study Hyperbolic Geometry?

Non-Euclidean Themes by Artist/Mathematician, Clifford Singer.

References & Further Reading.

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