Euclidean Geometry Flashcards
Planes have _____ dimensions
2
Lines have ______ dimensions
1
Points have _______ dimensions
0
A point is ______
A location represented by a dot with no length or width or thickness, named with a capital letter, undefinable
A line is
A figure with length but no width, a series of points, extends indefinitely in both directions, named with two capital letters with a line on top or with one lowercase letter, undefinable.
A plane is
flat surface made of infinite lines, extends in all directions, no thickness but length and width, named by a capital letter in script or three noncollinear points on the plane, undefinable
definition
a formal statement declaring the meaning of a word
postulate
a mathematical statement taken as fact (assumption)
theorem
a mathematical statement proven using postulates and definition
diagram
a visual tool representing mathematical ideas to be interpreted
point existence postulate
a line contains at least two points
collinear
on same line
unique line postulate
through any two points there is only one line
flat plane postulate
if two points are in a plane, then the line connecting those two is on the plane
parallel postulate
Through a given point not on a line, there exists exactly one line parallel to the given line through the given point.
conditional statement
if p (hypothesis) then q (conclusion) (p –> q)
converse
if q (conclusion) then p (hypothesis), symmetrical to conditional (q –> p)
inverse
if not p (hypothesis), then not q (conclusion) (~p –> ~q)
contrapositive
if not q (conclusion), then not p (hypothesis) (~q –> ~p)
the only time a conditional statement is false
when p (hypothesis) true but q (conclusion) false
the only time a converse is false
when p is false and q is true
the only time an inverse is false
~p is true and ~q is false
the only time a contrapositive is false
~p is false and ~q is true
- truth values for ___ and _____ are same
converse/conditional statement, inverse/contrapositive
logically equivalent =
reverse p and q but dont reverse ~
angle
two rays with a common endpoint
rays
lines that go infinitely in one direction but not the other
p ^ q
p and q (p is not hypothesis, neither is q)
symmetric property
a = b –> b = a
and
p v q
p or q (neither p or q is hypothesis) (the “or” is one or the other or both)
compound statement
2 or more statements connected by “and” or “or”
biconditional statement
can be written in the form (p if and only if q) or written in the form (if p then q, and if q then p)
