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... of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transver ...
... of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transver ...
course title – unit x - Douglas County School System
... #3—Uses visualization skills to explore and interpret both two- and three- dimensional geometric figures using such topics as projections, cross sections, and locus problems ...
... #3—Uses visualization skills to explore and interpret both two- and three- dimensional geometric figures using such topics as projections, cross sections, and locus problems ...
Non-Euclidean Geometry
... Definition 3. A pencil of lines consists of all lines which (i) intersect in a common point; (ii) are parallel to a given line; or (iii) have a common perpendicular. Let x, y be two lines of a pencil. Then if x and y intersect in a point P , the product σy σx is a “rotation” ρP,α about the point P t ...
... Definition 3. A pencil of lines consists of all lines which (i) intersect in a common point; (ii) are parallel to a given line; or (iii) have a common perpendicular. Let x, y be two lines of a pencil. Then if x and y intersect in a point P , the product σy σx is a “rotation” ρP,α about the point P t ...
History of geometry
Geometry (from the Ancient Greek: γεωμετρία; geo- ""earth"", -metron ""measurement"") arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic).Classic geometry was focused in compass and straightedge constructions. Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today. His book, The Elements is widely considered the most influential textbook of all time, and was known to all educated people in the West until the middle of the 20th century.In modern times, geometric concepts have been generalized to a high level of abstraction and complexity, and have been subjected to the methods of calculus and abstract algebra, so that many modern branches of the field are barely recognizable as the descendants of early geometry. (See Areas of mathematics and Algebraic geometry.)