Theorems - Venema

# Theorems - Venema - Theorems Venema Chapter 3 Theorem 3.1.7...

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Theorems – Venema Chapter 3 Theorem 3.1.7 If l and m are two distinct, non parallel lines, then there exists exactly one point P such that P lies on both l and m . [note that this is not true in Spherical geometry] p. 37 Theorem 3.2.7 If P and Q are any two points, then 1. PQ = QP, 2. PQ 0, and 3. PQ = 0, if and only if P = Q . p. 38 Corollary 3.2.8 A*C*B if and only if B*C*A . Theorem 3.2.16 The Ruler Placement Postulate For every pair of distinct points P and Q , there is a coordinate function f : PQ uur s R such that f ( P ) = 0 and f ( Q ) > 0. p.41 Theorem 3.2.17 Betweeness Theorem for Points Let l be a line; let A , B , and C be three distinct points on l; let f : PQ uur s R be a coordinate function for l . The point C is between A and B if and only if f (A) < f (C) < f (B) or f (A) > f (C) >f (B). p. 42 Corollary 3.2.18 Let A , B , and C be three distinct points such that B lies on AC uuur . Then A*B*C if and only if AB < AC. Corollary 3.2.19

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## This note was uploaded on 02/22/2012 for the course MATH 3379 taught by Professor Staff during the Spring '08 term at University of Houston.

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Theorems - Venema - Theorems Venema Chapter 3 Theorem 3.1.7...

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