HW4key - MATH 5397 HW4 Things that are the same in...

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MATH 5397 HW4 Things that are the same in Euclidian geometry and Spherical Geometry 1. Both systems are axiomatic in nature 2. Both systems share the 16 neutral geometry axioms 3. Both systems include polygons with 3 or more sides (Triangles, Quadrilaterals, Pentagons, etc.) with the same definitions. 4. Both systems have circles and have the same definition for circles 5. Both systems have a Pythagorean Theorem, although the formulas are different. 6. Both systems have congruence shortcuts for triangles 7. Angles in both systems are measured in either degrees or radians. Both have right angles. Angles are measured with protractors in both. 8. For any given line AB, at least one perpendicular line exists through each point between A and B. 9. Both geometries have the concept of congruence. 10. Shortcuts to triangle congruence: ASA, SSS, AAS work in both 11. When two perpendicular lines meet they divide both geometric planes into 4 congruent regions. 12. Reflection symmetry exists in both. 13. We measure distance by using the shortest distance between the two point sets in both. 14. Vertical angles are congruent in both geometries. 15. Both geometries have ways to measure area.
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Things that are the different in Euclidian geometry and Spherical Geometry 1. Differences in the axioms Incidence axiom 1 is not always true in spherical geometry. In EG, each two distinct points determine a line. In SG, if the two points are antipodal, the two
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HW4key - MATH 5397 HW4 Things that are the same in...

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