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 inters
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 set
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
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
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 o
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 a
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 equid
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
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
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