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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 one-to-one 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
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
if any lines of the polygon do contain interior points, the polygon is called concave,
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
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
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
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
set of points that consists of a segment
The Ruler Postulate
(postulate 7)
There is a one-to-one 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
a diagonal of a polygon is a segment that joins two nonconsecutive vertices of the polygon.
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
a set of points is a triangle iff is consists of the figure formed by three segments vonnevting three noncollinear point
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
the set of all points
perpendicular bisector of a segment
Line, ray segment, or plane that is perpendicular to a segment at its midpoint
statement accepted as true
interior angles
angles inside the lines being transversed
statement that must be proven true
no congruent sides
set of points on a line that consists of two points
Supplementary angles
Iff their sum=180
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.
theorem whose justification follows from another theorem
distance between the endpoints of the segment
obtuse triangles
one obtuse angle
segments having equal measures
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
three congruent angles
all sides congruent
Parallel lines
two lines are parallel iff they lie in the same plane and do not intersect
any line, segment, ray or plane that intersects a segment at its midpoint
exterior angles
angles outside the lines being transversed
(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
common endpoints of an angle
point that divides a segment into two congruent segments
two sides congruent
acute triangles
three acute angles
the union of two noncollinear rays
alternate exterior angles
a pair of non adjacent angles, both exterior, on opposite sides of the transversal
a line is a transversal iff it intersects two or more coplaner lines at different points