MAT 240 Quiz 3
What does Q^2 satisfy? - ANS-existence postulate and incidence postulate
What does Q^2 not satisfy? - ANS-Ruler Postulate
Convex - ANS-A set of points is called convex if for any pair of distinct points A,BeS,
|AB is a subset of S
Plane Separation Postulate - ANS-Given a line lcP, there exists sets H1 and Hs such
that:
1) H1=/ empty set H2=/ empty set
2) H1 U H2 = P-l
3) H1 & H2 = empty set
4) for all A,BeH1 (A=/B => |AB c H1)
5) for all A,BeH2 (A=/B => |AB c H2)
6) for all AeH1, for all BeH2: |AB & l =/ empty set
Same side of l - ANS-Let l be a line, let A,B be external points. If A&B lie in the same
half-plane (HA=HB) then A&B are on the same side of l. Otherwise, A&B are on
opposite sides of l.
Relation - ANS-Let l be a line. We define a relation on P-l as A~B <=> A&B lie on the
same side of l
Equivalence Relation - ANS-~ is an equivalence relation:
Reflexivity: For every AeP-l, A~A
Symmetry: For all A,BeP-l if A~B, then B~A
Transitivity: For all A,B,CeP-l if A~B and B~C then A~C
Opposite - ANS-Two rays AB and AC with common starting point A are called opposite
if line AB = line AC and ray AB does not equal ray AC
Rays AB and AC are opposite iff A,B,C are collinear and CxAxB
Angle - ANS-Let A,B,C be distinct points such that the rays AB and AC are
non-opposite. Then the angle <BAC is defined as <BAC= rayAB U rayAC
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