e2 - 6. (5 points) Give the statement of Playfairs...

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Name: Math 402 - Test #2 - March 7, 2007 Time: 50 minutes. Write your answers on the blank paper provided. Start a new page for each problem and be sure to number the problems. You may not use any books or notes. There are 100 points possible. 1. (7 points) Give the definition of similar triangle. 2. (7 points) Let f be a transformation. Define “ P is a fixed point of f .” 3. (5 points each part) Decide whether each of the following is an isometry or not. Give a brief explanation of your reasoning. You are not asked for a formal proof. (a) f ( x,y ) = ( - x,y ) (b) f ( x,y ) = ( x 2 ,y 2 ) (c) f ( x,y ) = ( x + 1 ,y + 2) 4. (10 points) Give the statement of Pasch’s Axiom. 5. (15 points) Prove that a line intersecting one side of a rectangle, at a point other than one of the vertices of the rectangle, must intersect another side of the rectangle.
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Unformatted text preview: 6. (5 points) Give the statement of Playfairs Postulate. 7. (25 points) Prove that the statementTwo lines that are parallel to the same line are coincident (the same) or themselves parallel implies Playfairs Postulate. 8. (4 points each part) Answer True or False for each part. No explanation is needed and there is no partial credit. (a) If an isometry has two distinct xed points, then it has an innite number of xed points. (b) Every isometry has at least one xed point. (c) The image of a parallelogram under an isometry is a parallelogram. (d) It is possible to prove Playfairs Postulate from Euclids ve postulates....
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This note was uploaded on 08/08/2009 for the course MATH 1 taught by Professor Malkin during the Spring '09 term at University of Illinois at Urbana–Champaign.

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