9.1 (Difference of angles). Suppose we are given congruent angles LBAC = LB'A'C'. Suppose also that we are given a ray AD in the interior of LBAC. Then there exists a ray A'D' in the interior of LB'A'C' such that LDAC LD'A'C' and LBADLB'A'D'. This statement corresponds to Euclid's Common Notion 3: "Equals subtracted from equals are equal," where "equal" in this case means congruence of angles. مراه A B с B
9.1 (Difference of angles). Suppose we are given congruent angles LBAC = LB'A'C'. Suppose also that we are given a ray AD in the interior of LBAC. Then there exists a ray A'D' in the interior of LB'A'C' such that LDAC LD'A'C' and LBADLB'A'D'. This statement corresponds to Euclid's Common Notion 3: "Equals subtracted from equals are equal," where "equal" in this case means congruence of angles. مراه A B с B
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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[Geometry] How do you solve 9.1?
Transcribed Image Text:9.1 (Difference of angles). Suppose we
are given congruent angles LBAC =
LB'A'C'. Suppose also that we are given
a ray AD in the interior of LBAC. Then
there exists a ray A'D' in the interior of
LB'A'C' such that LDAC
LD'A'C'
and LBADLB'A'D'. This statement
corresponds to Euclid's Common Notion
3: "Equals subtracted from equals are
equal," where "equal" in this case
means congruence of angles.
9.2 Suppose the ray AD is in the interior of
the angle LBAC, and the ray AE is in
the interior of the angle LDAC. Show
that AE is also in the interior of LBAC.
مراه
9.4 Provide the missing betweenness argu-
ments to complete Euclid's proof of (1.7)
in the case he considers. Namely, as-
suming that the ray AD is in the inte-
rior of the angle LCAB, and assuming
that D is outside the triangle ABC, prove
that CB is in the interior of the angle
LACD and DA is in the interior of the
angle LCDB.
A
A
B
с
A
B
D
9.3 Consider the real Cartesian plane where congruence of line segments is given by the
absolute value distance function (Exercise 8.7). Using the usual congruence of angles
that you know from analytic geometry (Section 16), show that (C4) and (C5) hold in
this model, but that (C6) fails. (Give a counterexample.)
E
D
B
B
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