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Geometry
Explore plane geometry; coordinates and transformations; space and geometry beyond euclid. Concepts and connections are available independently of video coverage.
Prerequisites and connections
Sets
A set is a collection of distinct objects; membership is different from inclusion.
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Plane geometry
Angles
An angle measures rotation between rays sharing an endpoint.
Video explanations to be addedTriangle congruence
Congruent triangles have matching sides and angles under a rigid motion.
Video explanations to be addedTriangle similarity
Similar triangles have equal corresponding angles and proportional corresponding sides.
Video explanations to be addedPythagorean theorem
In a right triangle, squared leg lengths sum to the squared hypotenuse length.
Video explanations to be addedCircle geometry
Chord, tangent and inscribed-angle relations connect angles and distances in a circle.
Video explanations to be addedArea and volume
Area measures planar regions and volume measures spatial regions in corresponding squared or cubed units.
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Coordinates and transformations
Coordinate geometry
Coordinates translate geometric conditions into equations and algebraic calculations.
Video explanations to be addedDistance formula
Euclidean distance is the square root of the sum of squared coordinate differences.
Video explanations to be addedLines and planes
Linear equations and vector representations describe straight lines and planes.
Video explanations to be addedConic sections
Ellipses, parabolas and hyperbolas arise from planar sections of a cone.
Video explanations to be addedRigid motions
Translations, rotations and reflections preserve Euclidean distances.
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Space and geometry beyond Euclid
Polyhedra
A polyhedron has polygonal faces meeting along edges and vertices.
Video explanations to be addedSolid geometry
Spatial geometry studies incidence, distance and angles among three-dimensional objects.
Video explanations to be addedGeometric projections
A projection maps spatial objects to a lower-dimensional view according to a chosen rule.
Video explanations to be addedNon-Euclidean geometry
Changing the parallel-postulate setting yields geometries with different angle and distance behavior.
Video explanations to be addedGeometric loci
A locus consists of all points satisfying specified geometric conditions.
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