Denition 38 Triangular region is the union of a triangle and its interior. Denition 39 A polygonal region is the union of a nite number of triangular regions such that if two triangular regions intersect, their intersection is an edge or vertex of both. D
Denition 7 Logical System consists of undened terms, denitions, assumptions and theorems. The undened terms for geometry are set, point, line, plane. Denition 8 One-to-one correspondence is if two sets have the same number of elements. If two sets have a
Postulate 12 Space separation postulate [4.5.ss-1] Given a plane in space. The set of all points that do not lie in the plane is the union of two sets S1 , S2 (the book uses H1 and H2 we will reserve those for half-planes) such that each of the sets is co
Theorem 14 Segment construction [3.6.C-2] Given a segment AB and a ray CD, there is exactly one point E on CD such that AB CE . = Theorem 15 Segment Addition [3.6.C-3] If A B C and D E F and AB DE and = BC EF then AC DF . = = Denition 22 Convex A set G is
Denition 12 Segment If A and B are two points then the segment between them is the set of points A X B , for all X in S , along with A and B . It is written AB Denition 13 Ray Is the set of points C on AB with A not between B and C . It is written AB . De
Denition 33 polygon A polygon is the union of n segments in a plane, intersecting at and only at their endpoints, such that exactly two segments contain each endpoint and no two consecutive segments are on the same line. We are going to assume that any po
Theorem 29 If A and B are equidistant from P and Q then every point between A and B has the same property. Theorem 30 If a line L contains the midpoint of P Q and contains another point which is equidistant from P and Q, then L P Q.
Theorem 40 Through a g
Denition 28 Parallel Two lines are parallel in a plane if they dont intersect. Postulate 16 Parallel Postulate Through a point not on a given line there is exactly one parallel to the line. Postulate 17 Lobachevsky and Bolya Postulate Through a point not
An axiomatic system example. Assume that a club of two or more students is organized into committees in such a way that each of the following conditions are satised. a) Every committee is a set of one or more students. b) For each pair of students, there
Homework 7 Identify the congruent triangles and show they are congruent. Note a picture can have more than one pair of triangles.
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Denition 1 Negation If p is a statement, the statement p is the negation of p. Example 1 Form the negation of the following statements. a The moon is rising. b ABC is a remote interior angle. c Point C is between points A and B . d m 3 = 25 Solution a The