Download Definitions and Theorems (Kay)

Definitions and Theorems (Kay):
You need to know the following definitions and theorems, as stated in your textbook.
You may have two pages of notes (front and back, so four sides total) for the in class
midterm, and there are no restrictions - you're free to note any and all of these down that
you can fit. My suggestion would be that you look them over and see if any of the
definitions in particular have something strikingly different than what you're used to. For
example, I probably wouldn't need to note down the definition of acute angle, because
Kay's definition is simply an angle that measures less than 90 – exactly what I'd expect –
but I'd be very inclined to write the definition of betweenness, because it's much more
precise and formal than what we usually go on (i.e. "looks") in Euclidean geometry.
I'm going to list these in order, and the order is important – you need to know where
something falls in the list to know what you're allowed to use in the proof of it. You
won't be asked to prove any of the theorems on the midterm, but you should be know
their formal statements, what they mean, and know the key dependencies within them
(e.g, the ASA and SSS congruence theorems depend on having the SAS postulate as part
of the axiomatic system).
Definitions
Axioms/Theorems
independence (of an axiomatic system) (p
65)
consistency (of an axiomatic system) (p
65)
categorical (p 66)
betweenness (for points) (p 79)
segment, ray, line, angle (p 81)
extension (p 82)
midpoint (p 85)
bisect (a segment) (p 85)
measure (of a segment) (p 85)
interior point (p 90)
betweenness (for rays) (p 91)
angle bisector (p 93)
opposing rays (p 95)
linear pair (p 95)
supplementary (p 95)
the incidence axioms for geometry (I-1
through I-5 in section 2.3) (pp 71-72)
the metric axioms (D-1 through D-3) (p
78)
ruler postulate (axiom D-4) (p 83)
(unnamed) theorem 3 on page 84
(unnamed) theorem 4 on page 84
segment construction theorem (p 85) and
its corollary (concerning the midpoint)
existency of angle measure (p 90)
angle addition postulate (p 91)
protractor postulate (p 93)
angle construction theorem (p 94) and its
corollary (concerning the bisector)
(unnamed) theorem 2 on p 96
complementary (p 95)
right angle (p 97)
perpendicular (p 97)
acute angle (p 98)
obtuse angle (p 98)
vertical angles (p 99)
convex (set) (p 104)
interior (of an angle) (p 108)
triangle, sides, and vertices (p 120)
congruence for segments and angles (p
122)
congruence for triangles (p 123)
properties of congruence (p 124)
isosceles triangle (p 142)
legs, base, vertex, vertex angles, base
angles of isosceles triangle (p 142)
linear pair axiom (p 96)
(unnamed) theorem 3 on p 98
vertical pair theorem (p 99)
plane separation postulate (p 105)
postulate of Pasch (p 107)
(unnamed) theorem 2 on p 108
crossbar theorem (p 109)
CPCF (also known as CPCTC) (p 123)
the SAS hypothesis (p 124) and SAS
postulate (p 140)
ASA theorem (p 141)
isosceles triangle theorem (p 142)
perpendicular bisector theorem (p 144)
SSS theorem (p 145)
exterior angle (of a triangle) (p 152)
opposite interior angles (relative to
exterior) (p 152)
exterior angle inequality (p 156)
Saccheri-Legendre theorem (p 160)
scalene inequality (p 166)
triangle inequality (p 167)
hinge theorem (SAS inequality) (p 169)
AAS congruence theorem (p 174)
SSA theorem (p 175)
quadrilateral terminology (p 183)
properties of convex quadrilaterals (p
183)
convex (p 183; defined precisely in lecture) congruence theorems for convex
quadrilaterals – SASAS, ASASA, etc (pp
184-185)
rectangle (p 186)
“theorem 2” and the other properties of
Saccheri quadrilaterals on p 187
Saccheri quadrilateral (p186)
Lambert quadrilateral (p 187)
circle terminology (p 194)
the circle properties on p 195
arc terminology (p 196)
additivity of arc measure (p 197)
tangent and secant (circles) (p 198)
the tangent theorem (p 198) and its
corollary (p 199)