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60 Cards in this Set
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The protractor postulate
(postulate 9) 
In a half plane with the edge AB and any point S between A and B, there exists a onetoone correspondence between the rays that originate at S in that half plane and the real number between 0 and 180. To measure an angle formed by two of these rays, find the absolute value of the difference of the corresponding real numbers.


Alternate interior angles

a pair of non adjacent angles , both interior, on opposite side of the transversal


postulate 5

* If two distinct planes intersect then their intersection is a line


unique

meaning exactly one or one


Linear Pair postulate
(postulate 10) 
If two angles form a linear pair, then they are supplementary angles.


parallel planes

two planes are parallel iff they do not intersect


Postulate 3

* through any two points there are infinitely many planes.
* Through any three points there is at least one plane * Through any three noncollinear points there is exactly one plane 

half plane

two halfs of plane that are seperated by a line


Concave

if any lines of the polygon do contain interior points, the polygon is called concave,


polygons

a polygon consists of three or more coplaner segments; the segments, sides, intersect only at the endpoints; each endpoint, vertex belongs to exactly two segments; no two segments with a common endpointare collinear


Postulate 4

* If two points are in a plane, then the line that contains those points lies entirely in the plane


between

given three collinear points x,y,z, y is between x and z iff xy+yz=xz


postulate 6

* given any two points there is a unique distance between them


convex

a polygon is convex iff the lines containg teh sides do not contain points in the polygon interior


Postulate 1

* a line contains at least two distinct points
* A plane contains at least three noncollinear points * Space contains at least four noncollinear points 

Point

has no size or dimension, merely a position indicator. Points are names by upper case letters.


regular polygon

a polygon is a regular polygon iff it is both equilateral and equilangular


parallel segments or rays

segments or rays are parallel iff the lines that contain them are parallel


Postulate 2

* Two distinct points determine a unique line


ray

set of points that consists of a segment


The Ruler Postulate
(postulate 7) 
There is a onetoone correspondence between the points of a line and the set of real numbers such that the distance between two distinct points of the line is the absolute valuse of the difference of their coordinates


linear pair

adjacent angles whose noncommon sides are opposite rays


Diagonal

a diagonal of a polygon is a segment that joins two nonconsecutive vertices of the polygon.


intersection

the set of points that lie in both figures


postulate 8

* Given any angle there is a unique real number between 0 and 180 known as its degree measure


Triangle

a set of points is a triangle iff is consists of the figure formed by three segments vonnevting three noncollinear point


plane

a flat surface with no defined thickness that extends without end in all directions. Usually pictured as a four sided figure. Named with a Capitol letter or with any thre non collinear points.


vertical angles

two nonadjacent angles formed by two intersecting lines


space

the set of all points


perpendicular bisector of a segment

Line, ray segment, or plane that is perpendicular to a segment at its midpoint


postulate

statement accepted as true


interior angles

angles inside the lines being transversed


Theorem

statement that must be proven true


scalene

no congruent sides


segment

set of points on a line that consists of two points


Supplementary angles

Iff their sum=180


line

consists of an infinate number of points, and extends in both directions without end. Name lines with 2 points from the line or with a lower case letter.


corollary

theorem whose justification follows from another theorem


measure

distance between the endpoints of the segment


obtuse triangles

one obtuse angle


congruent

segments having equal measures


perpendicular

two lines that intersect to form right angles


right triangles

on right angle


auxiliary line

lines, segments, rays or points added to a figure in order to facilitate a proof or an understanding of a problem. Their introduction must be justified by a postulate or theorem


equilangular

three congruent angles


equilateral

all sides congruent


Parallel lines

two lines are parallel iff they lie in the same plane and do not intersect


bisector

any line, segment, ray or plane that intersects a segment at its midpoint


exterior angles

angles outside the lines being transversed


adjacent

(next to) have to have a common side, common vertex, no interior points


corresponding angles

a pair of nonadjacent angles, one interior, one exterior, both on the same side of the transversal


skew lines

twon lines are skew iff they do not lie in the same plane and do not intersect


Complementary angles

Iff their sum=90


vertex

common endpoints of an angle


midpoint

point that divides a segment into two congruent segments


isosceles

two sides congruent


acute triangles

three acute angles


angle

the union of two noncollinear rays


alternate exterior angles

a pair of non adjacent angles, both exterior, on opposite sides of the transversal


Tranversal

a line is a transversal iff it intersects two or more coplaner lines at different points
