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Download Math 362 - Section 001 Fall 2006 Practice Test 1
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Name: Math 362 - Section 001 Fall 2006 Practice Test 1 Closed Book / Closed Note. Write your answers on the test itself. Part I: Circle T if the statement is true, and F if the statement is false. 1. Euclid’s work is important mainly because he discovered many new geometrical facts. T F 2. David Hilbert developed an axiom system for geometry that filled in many of the “holes” in Euclid’s system. T F 3. So called “synthetic” geometry does not rely on other mathematical systems such as real numbers. T F 4. The undefined terms in our axiom system include point, line, plane, lies on, and distance. T F 5. The Postulate of Pasch in equivalent to the Plane Separation Postulate. T F 6. The Ruler Postulate establishes a single coordinate function that works for every line. T F 7. If a statement and its negation can both be proved within an axiom system, that statement is said to be independent. T F 8. Any statement that is proveable within an axiom system is true in every model of that system. T F 9. In the early 1900's a group of European mathematicians who published under the name of Nicolas Bourbaki standardized the axioms of geometry so that now every textbook uses the same axiom system. T F 10. The Protractor Postulate establishes a one-to-one correspondence between non-negative real numbers less than 180, and a set of angles. T F Section II: Matching Match the Postulate on the left with the description on the right by writing the letter of the correct description in the blank after each statement. 11. Postulate of Pasch A. Establishes how lines and points interact with one another. 12. Crossbar Theorem B. Establishes a metric or distance function. 13. Ruler Postulate C. Guarantees that your geometry is not empty. 14. Incidence Postulate D. Is equivalent to the Plane Separation Postulate. 15. Linear Pair Theorem E. Guarantees that a ray between will intersect point. 16. Existence Postulate F. and at an interior Establishes the relationship between linear pairs and supplementary angles. Section III: Short answer. 17. A model for Incidence Geometry has points S = {1, 2, 3, 4} and lines {1, 2}, {1, 3}, {1, 4}, and {2, 3} (among others). What sets must the remaining lines be? 18. Consider the model: Points: S= { 1, 2, 3, 4, 5}; Lines: {1, 2, 3, 4}, {1, 5}, {2, 5}, {3,4}, {3, 5}, {4, 5}. Is this a model for Incidence Geometry? Explain briefly. 19. Suppose that K, L, and W are three points lying on a line, with ruler coordinates 3, 5, and x, respectively. If KW =5 and LW = 7, what are the possible values for x? 20. Rays on one side of form angles with measures of pCBF, pDBC, and pEBD as indicated in the figure. Ray is opposite ray the betweeness relations evident in the figure, find a. mpABG b. mpGBD , and is opposite . Using 21. pQMN and pQMP are a linear pair of angles. Rays pQMP, respectively. Find: µpQMX + µpQMY. 22. Two lines meet at a point M, with A-M-B and C-M-D. Identify the shaded region in the figure in terms of half-planes, with unions and/or intersections as appropriate. and bisect pQMN and 23. Use the language of angle interiors (along with unions and intersections) to describe the shaded region in the figure. 24. Consider the following relationships among three angles: p1 is complementary to p2, p1 is supplementary to p3, and the sum of the measures of p2 and p3 equals 120. Find mp2. 25. Point B lies on the ray opposite ray and you are given that µpABC = 40 and µpABE = 160. In addition, bisects pABC. What values are possible for µpDBE?