Euclidean and Transformational Geometry: A Deductive Inquiry
Jones & Bartlett Publishers, 12.02.2008 - 371 Seiten
Ideal for mathematics majors and prospective secondary school teachers, Euclidean and Transformational Geometry provides a complete and solid presentation of Euclidean geometry with an emphasis on solving challenging problems. The author examines various strategies and heuristics for approaching proofs and discusses the process students should follow to determine how to proceed from one step to the next through numerous problem solving techniques. A large collection of problems, varying in level of difficulty, are integrated throughout the text and suggested hints for the more challenging problems appear in the instructor's solutions manual and can be used at the instructor's discretion.
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Congruence Constructions and the Parallel Postulate
Area and the Pythagorean Theorem
Isometries and Size Transformations
Composition of Transformations
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ABCD altitudes angle bisector Axiom bisect chord circle with center circumscribing collinear complex numbers composition construct coordinate Corollary corresponding diagonals diameter distance endpoints equal Equation equilateral triangle Euclid’s Euclidean geometry exterior angle Exterior Angle Theorem following theorem formula geometry given gles glide reflection golden ratio hence hypotenuse implies Inscribed Angle interior isometry Justify your answer kite length line intersects line parallel mathematician measure medians midpoint midsegment Nine-Point Circle Notice opposite sides pair Parallel Postulate parallelogram pedal triangle perimeter perpendicular bisector polygons Problem Set proof properties Pythagorean Theorem quadrilateral radius ratio real number rectangle rhombus right angle right triangle rotation shown in Figure similar solution Solve square symmetry tangent transformation translation trapezoid triangle ABC triangles are congruent vector vertex vertices x-axis α α α β