MAT 360: Geometric Structures Spring 2010 | |
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Homework assignments for MAT 360Assignment 10. Due date April 29From the textbook: 356, 358, 378, 395, 425. Assignment 9. Due date April 27Assignment 8. Due date April 81. Find a line intersecting two given lines and parallel to a third one. How does the number of such lines depend on the given three lines? 2. Let AB and CD be skew lines. Prove that midpoints of the segments AC, AD, BC and BD form a parallelogram, and that its plane is parallel to the lines AB and CD. 3. Find a line perpendicular to two given skew lines. How many such lines exist. 4. Find the locus of points equidistant in the space from two given points. 5. Find the locus of points in the space equidistant from given three points which do not lie on the same line. Assignment 7. Due date March 25From the textbook: 305, 306, 314, 320. Assignment 6. Due date March 181. Given three lines l, m, n meeting at one point and a point A on l, construct a triangle ABC such that the lines l, m, n are its bisectors. 2. Construct a regular triangle having vertices on three given parallel lines l, m, n. 3. Construct a quadrilateral ABCD such that its diagonal AC is the bisector of its angle A and the sides are congruent to given four segments. 4. Construct a triangle with given angle A, side a opposite to A, and altitude h_{a} dropped from A. 5. Construct a triangle with given side a, difference b-c between the other two sides and angle B opposite to the side B. Assignment 5. Due date March 4From the textbook: 231, 236. Although it is not included into the home assignement, prepare yourself to the midterm on March 4. Take a look at the practice midterm1 and revisit the following sections of the textbook: 35, 36, 40, 42-45, 48-52, 70-73, 75-81, 83-87, 93, 95, 104-108, 111-113, 122-124, 126. Assignment 4. Due date February 23
Solutions for the following problems should be made of the following parts:
1. Given circles c and d, segment s and line l, construct a segment AB such that A lies on c, B lies on d, AB || l and AB is congruent to s. 2. Given a circle c, line l and point O, construct a segment AB such that A lies on c, B lies on l and O bisects AB. From the textbook: 211 (a), (c), 222. Assignment 3. Due date February 16180, 183, 189, 199, 203. Assignment 2. Due date February 91. Prove that in a triangle ABC, vertices A and B are equidistant from the median CM. From the textbook: (The problems are reproduced below)
Assignment 1. Due date February 2
1. Read pages 1-18 of the textbook (contained in the the sample pages).
List all the encounters of implicit usage of the properties
of congruences.
Other properties were formulated in the first lecture: In other words, Thus the task is to find all the places in the first 18 pages of the
textbook, where these properties are used implicitly, that is
without explicit mentioning. Present a solution in the form of a table
with lines: The rest of the assignemt is the following problems from the textbook: 61, 63, 67. |
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