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73 Cards in this Set

  • Front
  • Back
Parallel
2 objects are // iff they dont intersect
Distinct
2 distinct pts determine a line iff there is one line containing those 2 pts
concurrent
2 objects or more meet iff their intersection is nonempty
Coplanar/collinear
2 or more pts are collinear iff there is a single place/line containing them
indirect proof
A proof by contradiction where you assume p and ~q. Then try to find thr contradiction
I1
Any 2 distinct pts determine a line
I2
Any 3 noncollinear pts determine a plane but just one plane
axioms
Are mathematical statements accepted without proofs
Distance axioms
d1-d4
D1
For any 2 pts A, B there is a unique real # called DISTANCE from A to B, AB
triangle inequality
For any 3 points A, B, C, AB+BC>=AC
d3
For any point A, B, AB=BA
d2
For any points A, B, AB>=0 and AB=0 iff A=B
model
Given a set of axioms, for that set is a mathematical example in which the axioms hold truth
converse
Given p-q the converse is q-p
betweeness
Given pts A, B, C we say that B is between A & C iff
1) ABC are distinct
2) ABC are collinear
3) AB+BC=AC
I4
If 2 distinct planes meet their intersection is a line
I3
If a plane contains 2 pts then it contains every line thru those 2 points
unprovable
If a statement fails to be true in any one model for a set of axioms, the statement is unprovable
Independent
If for any one axiom there is a model in which that axiom fails but all others hold
consistent
If there is no statement that can be proven or disproven
Conjecture
if...then
incidence axioms
I1-i5
properties of axioms
Independence( not redundant)
Consistency (no contradiction)
orthocenter
Intersection of the 3 altitudes of a triangle
contrapositive
Is ~q-~p to the p-q
orthocenter
Lie on side but not vertex is right
Outside obtuse
circumcenter properties
Midpoint of hypotenus is right triangle
Outside is obtuse
Inside is acute
Logically equivalent
P and q are this if p-q and q-p are both true
circumcenter
Point where the perpendicular bisectors of a triangle intersect
Undefined terms
Point, line, plane, space
Angel ABC
Ray BA U Ray BC provided A, B, C are not collinear
I5
Space consist of at least 4 noncoplanar pts and at least 3 noncollinear. Every plane contains at least 3 noncol pts abd at least 2 pts
Direct proof
Start from p use def, thms to arrive to q
Proof by contrapositive
To prove p-q instrad prove ~q-~p (dont assume p, proving p is false)
incenter
Where the angle bisectors intersect which is only inside the triangle
Ray AB
{X|A-X-B or A-B-X or X=A or X=B}
Segment AB
{X|A-X-B or X=A or X=B}
line AB THM
if A&B are distinct points then line AB ={X|A-X-B or X-A-B or A-B-X or X=A or X=B}
segment construction thm
if segment AB and segment CD are two segments w/AB <CD then there is a point E on segment CD so that C-E-D and CE=AB
angle ABC
A, B, C not collinear < ABC =ray AB U ray BC
a point is interior to an angle
a point D is interior to angle ABC iff there exists points E on ray BA and F on ray BC neither equal to B so that E-D-F holds
one Ray is between two others
ray BD is between rays BA and BC written ray BA - ray BD-ray BC iff these rays are distinct and m< ABD + m<DBC= m<ABC
two angles form a linear pair
iff they share one side and other side are opposite rays
vertical pair thm
vertical angles have the same measure
supplementary
180
complementary
90
a set is convex
iff whenever A and B are distinct pts in K all segments AB lies in K
triangle ABC
given 3 non collinear pts A, B, C triangle ABC is the set =segment AB U segment AC U segment BC
congruent
segments AB and XY are congruent AB=XY
Angles 1 and 2 are congruent if m<1 = m<2
triangles abc and xyz are congruent iff angle a=Angle x, b=y, c =z
ab=xy, ac=xz, bc=yz
SAS
let triangle abc and xyz be two triangles so that two sides and their included one angle of triangle abc are congruent to the corresponding two sides and angles of triangle xyz under a approach x and b approach y and c approach z then triangle abc is congruent to triangle xyz
Euler segment
orthocenter
incenter
circumcenter
a point D is interior
to <ABC iff there exists pts E on ray BA and F on ray BC neither equal to B so that E-D-F holds
ray BD is between
rays BA and BC written RAY BA- RAY BD- ray BC iff these rays are distinct and m<ABD + m<DBC= m<ABC
a side of a line
protractor postulate A3
linear pairs
two angles form a linear pair iff they share one side and the other side are opposite rays
opposite rays
if A-B-C hold then ray BA and Ray Bc are called this
if abc and bcd hold then abcd holds
plane separation axiom H1
triangle abc
congruence
SAS
crossbar thm
postulate of pasch
angle construction thm
segment construction thm
thm
thm
thn of union