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Plane Euclidean GeometryEdit
Euclidean geometry is the form of geometry defined and studied by Euclid. It is generally distinguished from nonEuclidean geometries by the parallel postulate, which (in Euclid's formulation) states "that, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles".
This section covers theorems that relate to Euclidean geometry in two dimensions.
Name of Topic  Subtopics 

Lines and Angles  Parallel Lines 
Polygons  Triangles, Pythagorean Theorem, Quadrilaterals, Polygon Construction 
Trigonometry  Basic Trigonometry, Sine and Cosine Rules, Trigonometrical Identities 
Curves  Circles, Conic Sections 
Coordinate Geometry  Plane Cartesian Coordinates, Plane Polar Coordinates, Coordinate Transformations 
Solid Euclidean GeometryEdit
This section covers theorems that relate to Euclidean geometry in three dimensions. Many proofs in threedimensional geometry rely on results in plane geometry.
Name of Topic  Subtopics 

Lines, Planes and Angles  
Polyhedra  Platonic Solids, Archimedean Solids 
Curved Solids and Surfaces  Spheres, Cylinders, Cones, Quadrics 
Projective GeometryEdit

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Elliptic GeometryEdit

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Elliptic geometry is a nonEuclidean geometry in which there are no parallel straight lines – any coplanar straight lines will intersect if sufficiently extended. The surface of a sphere, considered as a geometric space in its own right, exhibits this kind of geometry.
Hyperbolic GeometryEdit

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Hyperbolic geometry is a nonEuclidean geometry in which every straight line has a continuum of parallel straight lines (in the 'never meeting' sense) through the same point.