Wha 3. Suppose that in a certain metric geometry satisfying Axioms D-1-D-3, points A, B, C. and D are collinear, and AD = 6, %3D BC = 8, %3D AB = 4 = AC, BD = 9, CD = 1. (a) What betweenness relations follow (by definition) among these points? ) Show that the Triangle Inequality is not satisfied. The expressions on the left represent certain geometric objects that right (For example, Figure (I) s
Wha 3. Suppose that in a certain metric geometry satisfying Axioms D-1-D-3, points A, B, C. and D are collinear, and AD = 6, %3D BC = 8, %3D AB = 4 = AC, BD = 9, CD = 1. (a) What betweenness relations follow (by definition) among these points? ) Show that the Triangle Inequality is not satisfied. The expressions on the left represent certain geometric objects that right (For example, Figure (I) s
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please anwer question 3(2.4) This is a math problem.
Transcribed Image Text:AXIOM D-2: For all points A and B, AB 0, with equality only when
AXIOM D-1: Each pair of points A and B is associated with a unique real
Foundations of Geometry 1
Metric Axioms
a
number, called the distance from A to B, denoted by AB.
AXIOM D-2: For all points A and B, AB 2 0, with equality only wh
A = B.
AXIOM D-3: For all points A and B, AB = BA.
Transcribed Image Text:1. that in a certain metric geometry satisfying Axioms D-I-D-4. points A, B,
What betweenness relations follow (by definition) among these points? (A diagram
What betweenness relations follow (by definition) among these points?
2. Suppose that in a certain metric geometry satisfying Axioms D-1-D-3, points A, B,
eROBLEMS (2.4
GROUP A
ВС
8.
%3D
BD = 3,
AB= 4 = AC.
CD 5,
and
C. and D are collinear, and
ВС 3D 6,
BD = 3 = CD
%3D
AB = 4 = AC,
%3D
%3D
and
AD = 2.
C. and D are collinear, and
AD = 6,
BC = 8,
BD = 9,
%3D
CD = 1.
AB = 4 = AC,
) Show that the Triangle Inequality is not satisfied.
4 Matching The expressions on the left represent certain geometric objects that are
nictured in their totality in the figures on the right. (For example, Figure (1) shows
the geometric object SR.) For each expression, enter the number of the matched
netric object. The same response may be used more than once.
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