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1. What is the nature of parallel and perpendicular lines in Euclidean, Spherical, and Hyperbolic geometry?
2. What is the nature of the sum of the interior angles of a triangle in Euclidean, Spherical, and Hyperbolic geometry?
3. What is the concept of “betweenness” in Euclidean, Spherical, and Hyperbolic geometry?
4. In Spherical Geometry, know the nature of the spherical plane, including Great Circles (lines), points, segments, polygons and circles
5. Know the difference of properties of triangles between Euclidean, Spherical and Hyperbolic geometry including Pythagorean Theorem, Exterior Angles Theorem, and triangle similarity and congruency theorems.
6. In Spherical Geometry, know how to find the area of a lune (biangle) and small triangle (using Girard’s Theorem).
7. In Hyperbolic Geometry, know how to represent lines, segments, angles, and polygons using the Poincaré disk model.
8. In Hyperbolic Geometry, know how angles are measured. On the Poincaré disk model.
2. What is the nature of the sum of the interior angles of a triangle in Euclidean, Spherical, and Hyperbolic geometry?
3. What is the concept of “betweenness” in Euclidean, Spherical, and Hyperbolic geometry?
4. In Spherical Geometry, know the nature of the spherical plane, including Great Circles (lines), points, segments, polygons and circles
5. Know the difference of properties of triangles between Euclidean, Spherical and Hyperbolic geometry including Pythagorean Theorem, Exterior Angles Theorem, and triangle similarity and congruency theorems.
6. In Spherical Geometry, know how to find the area of a lune (biangle) and small triangle (using Girard’s Theorem).
7. In Hyperbolic Geometry, know how to represent lines, segments, angles, and polygons using the Poincaré disk model.
8. In Hyperbolic Geometry, know how angles are measured. On the Poincaré disk model.