
Chapter 1 Points and Lines
line segments
collinear points
concurrent lines
midpoint
circular definitions
undefined terms
postulates and theorems
coordinates of a point
Chapter 2 Angles
rays
Euclid’s The Elements
acute, right, and obtuse angles
congruent angles
degrees, minutes, and seconds
vertical angles
supplementary angles
linear pair
Chapter 3 Triangles
right triangles, hypotenuse, and legs
acute and obtuse triangles
isosceles triangles
scalene triangles
SSS, SAS, ASA postulates
drawing auxiliary lines
equilateral and equiangular triangles
Chapter 4 Parallel Lines
coplanar and skew lines
indirect proofs
exterior angles
alternate interior angles
corresponding angles
Chapter 5 Perpendicular Lines
theorems, propositions, lemmas, and
corollaries
HypotenuseLeg Theorem
perpendicular bisectors
medians
distance from a point to a line
Chapter 5½ Chain the Gate
P and Q
P or Q
P implies Q
Chapter 6 Quadrilaterals
parallelogram
trapezoid
rhombus
kite
rectangle
square
Honors Problem of the Century
midsegment of a triangle
intercepted segments
Chapter 7 Area
triangles
parallelograms
rectangles, rhombuses, and squares
perimeter
trapezoids
polygons
Pythagorean Theorem
Heron’s formula
triangle inequality
Chapter 7½ Junior Geometry and Other Little Tiny Theories
threepoint geometry
models for axiom systems
group theory
Chapter 8 Similar Triangles
AA postulate
proportions
generalization of the Midsegment
Theorem
altitudes
Angle Bisector Theorem
Chapter 8½ Symbolic Logic
contrapositive
¬ P (“not”)
truth tables
transitive property of implication
tautology
Chapter 9 Right Triangles
mean proportional, geometric mean
three famous right triangles: 3–4–5,
45º–45º–90º, 30º–60º–90º
tangent function
Chapter 10 Circles
center, radius, chord, diameter,
secant, tangent
concentric circles
central angles
arcs
inscribed angles
proof by cases
circumference
π
inductive and deductive reasoning
hunch, hypothesis, theory, and law
sectors
Chapter 11 Constructions
compass and straightedge
rules of the game
rusty compass constructions
golden rectangles and golden ratio
trisecting an angle
squaring a circle
incenter and circumcenter of a
triangle
collapsible compass constructions
46 popular constructions
Chapter 11½ NonEuclidean
Geometry
attempts to prove the Parallel
Postulate
Lobachevsky’s geometry
consistent mathematical theories
Riemann’s geometry
Chapter 12 Solid Geometry
a line perpendicular to a plane
distance from a point to a plane
parallel and perpendicular planes
polyhedrons
hexahedron (cube)
tetrahedron
octahedron
icosahedron
dodecahedron
Euler’s Theorem
volume formulas
Cavalieri’s Principle
lateral surface area
volume formulas:
cylinders, prisms, cones,
pyramids, and spheres
Chapter 12½ Geometry in Four Dimensions
how to tell what dimension you live
in
how twodimensional people “know”
that there is no third dimension
getting out of jail
organic chemistry and why you
don’t want to be flipped in the
fourth dimension
tesseracts and hypertesseracts
the Chart of the Universe (up to 14
dimensions)
Chapter 13 Coordinate Geometry
analytic geometry
Cartesian/rectangular/orthogonal
coordinate system
axes, origin, and quadrants
slope
distance formula
midpoint formula
proofs using analytic geometry
Chapter 13½ Flawless (Modern) Geometry
proof that every triangle is isosceles
proof that an obtuse angle is
congruent to a right angle
19yearold Robert L. Moore’s
modern geometry
e, π and √ –1
A.R.T. section
a quick summary of all
of geometry
Index 