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... 2. On the SAME graph, Plot D(-3, O)as triangle A’B’C’ A(2,1)(-3) maps to A’(-6, -3) B(3, 2)(-3) maps to B’ (-9, -6) C’(1, 3)(-3) maps to C’ (-3, -9) ...
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... 2. Use the Pythagorean Theorem to solve problems. A few episodes ago, we looked at determining whether ANY two triangles were congruent. To review, there were several combinations of sides and angles we needed to draw a conclusion. They were (in no particular order): ...
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... T (i) If a student is at van Hiele level 2, the student does not comprehend the significance of deduction as a whole or the role of axioms. Empirically obtained results are often used in conjunction with deduction techniques. T (j) In a regular polyhedron the same number of faces meet at each vertex ...
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Rational trigonometry

Rational trigonometry is a proposed reformulation of metrical planar and solid geometries (which includes trigonometry) by Canadian mathematician Norman J. Wildberger, currently an associate professor of mathematics at the University of New South Wales. His ideas are set out in his 2005 book Divine Proportions: Rational Trigonometry to Universal Geometry. According to New Scientist, part of his motivation for an alternative to traditional trigonometry was to avoid some problems that occur when infinite series are used in mathematics. Rational trigonometry avoids direct use of transcendental functions like sine and cosine by substituting their squared equivalents. Wildberger draws inspiration from mathematicians predating Georg Cantor's infinite set-theory, like Gauss and Euclid, who he claims were far more wary of using infinite sets than modern mathematicians. To date, rational trigonometry is largely unmentioned in mainstream mathematical literature.
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