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95 Cards in this Set

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the distance postulate
to every pair of different points there corresponds a unique positive number
The Ruler Postulate
To every point of the line corresponds exactly one real number, to every real number corresponds exactly one point on the line, and the distance between any two points is the absolute value of the difference of the corresponding numbers
The Ruler Placement Postulate
Given two points P and Q on a line, P is zero and the coordinate of Q is positive
The Line Postulate
For every two points there is exactly one line that contains both points
Every plane contains (points)
at least three noncollinear points
Space contains (points)
at least four noncollinear points
IF two points on a line lie in a plane, the the line
lies in the same plane.
The Plane Postulate
Any three points lie in at least one plane, and any three noncollinear points lie in exactly one plane.
If two plane intersect their intersection is a
line
To every angle there corresponds a number between
0-180
Angle Addition Postulate
Self-explanatory
The Supplement Postulate
If two angles form a linear pair, they they are supplementary
The SAS postulate
SAS congruence
ASA postulate
ASA congruence
SSS postulate
SSS congruence
the Parallel postulate
through a given external point there is only one parallel to a given line
The Area Postulate
To every polygonal region there corresponds a unique positive real number
The Congruence Postulate
If two triangles are congruent then their triangular regions have the same area.
The Area Addition Postulate
If two polygonal regions intersect only in edges and vertices (or do not intersect at all) then their area is the union of the sum of their areas.
The Unit Postulate
The area of a square region is the square of the length of its edges

The are of a rectangle is the product of the altitude and the area of the base
If A B and C are three different points of the same line then exactly one of them is
in between the other two
Given a line and a point not on the line
there is exactly one plane containing both.
Given two intersecting lines
there is exactly one plane containing it.
If two angles are complementary then they are
acute angles
If two angle are congruent and supplementary then each is a
right angle
The Supplement Theorem
supplements of congruent angles are congruent
The Complement Theorem
Complements of congruent angles are congruent
The Vertical Angle Theorem
Vertical angles are congruent
If two intersecting lines form one right angle
then they form four right angles
The Angle Bisector Theorem
Every angle has exactly one bisector
The Isosceles Triangle theorem
If two sides of a triangle are congruent then the angles opposite them are congruent.
Converse Isosceles Triangle Theorem
If two angles of a triangle are congruent then the sides opposite them are congruent
The Perpendicular Bisector Theorem
The perpendicular bisector of a segment in a plane is the set of all points of the plane that are equidistant from the end points of the segment
Parts theorem
the part is smaller than the whole
The Exterior angle theorem
exterior is greater than remote. In fact, exterior is the sum of the two remote.
the SAA theorem
SAA congruence
Hypotenuse leg Theorem
if the hypotenuse and one leg is congruent and it's a right triangle, they're congruent
Longer side angle theorem
Longer side is opp of larger side and smaller side smaller angle, if it's the same triangle.
If two angles of a triangle are not congruent then the sides
are not congruent
The first minimum theorem
the shortest segment is the perpendicular segment
the triangle inequality
the sum of the length of any two sides is greater than the length of the third side.
the Hinge theorem
If two sides of one triangle are congruent to two sides of another and the included angle of the first is larger, than the included angle of the second, then the side to the first one is longer to the other one.
Converse Hinge theorem
converse of hinge. but it's longer segment to angle instead of opposite.
Triangle Inequality
the sum of the length of any two sides of a triangle is greater than the length of the third side.
If B and C are equidistant from P and Q then every point between B and C is
equidistant from P and Q
if a line and a plane are perpendicular then the plane contains every line
perpendicular to the given point at its intersection with the given plane
the perpendicular bisecting plane theorem
the perpendicular bisecting plane of a segment is the set of all points equidistant from the end points of the segment
second minimum theorem
the shortest segment to a plane from an external point is the perpendicular segment
two parallel lines
lie in exactly one plane
alternate interior
congruent
corresponding angles
congruent
same side interior
supplementary
if two lines are parallel to same line, then they are
parallel to each other
the sum of the measures of a triangle is
180
in a parallelogram
opposite sides are congruent and consecutive angles are supplementary.
the diagonal of a parallelogram
bisects each other
in a quad., the two opp sides are congruent
it is a parallelogram
in a quad if a pair of sides are both parallel and congruent
its a parllelogram
if diagonals of a quad bisect each other
it's a parallelogram
in a rhombus the diagonals are
perpendicular to each other
midsegment theorem
midsegment is half and parallel to third side
in a quadrilateral if one right angle then
four right angle
if the diagonals of a quadrilateral bisect each other and are perpendicular then the
quad is a rhombus.
the median to the hypotenuse of a right triangle is
half as long as the hypotenuse
30-60-90
1, 2, square root of three
if one leg of a right triangle is half as long as the hypotenuse
the opposite angle has measure of 30
parallel lines are always
equidistant
area of trapezoid is
half the bases x altitude
if two triangles ahve the same bases and altitudes
they have the same area
if two triangles ahve the same altitude h, then the ratio of their areas
is the ratio of their bases
the pythag thereom
a^2 + b^2=C^2
converse pythag theroem
if using pythag theorem it fits, then it's a right triangle
the isosceles right triangle theorem
45-45-90 is 1-1-square root of 2
the basic proportionality theorem
if a line is parallel to one side of the triangle it creates similar triangles
if a line intersects and makes proportional segments then it is
parallel to third side
AA similarity theorem
triangles with this are similar
SAS similarity
triangles with this are similar
SSS similarity
triangles with this are similar
given a right triangle and the altitude of the hypotenuse
the altitude is the geometry mean of the segments into which it separates the hypotenuse

Each leg is the geometry mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg
If two triangles are similar then the ratio of their areas is the
square ratio of any two corresponding sides
a line perpendicular to a radius at its outer end is
tangent to the circle
every tangent to a circle is perpendicular to the
radius drawn to the point of contact
the perpendicular from the center of a circle to a chord
bisects the chord
the segment from the center of a circle to the midpoint of a chord which is not a diameter
is perpendicular to the chrod
the perpendicular bisector of a chord
passes through the center
in the same circle or in congruent circle any two congruent chords
are equidistant from the center
the line-circle theorem
if a line and circle are coplanar and the line intersects the interior of a circle then it intersects the circle in two and only two points
a plane perpendicular to the radius at the outer end
is tangent to the sphere
the arc addition theorem
you can add arcs
the inscribed angle theorem
the measure of an inscribed angle is half the measure of tis intercepted arc
in the same circle or in congruent circles, if two arcs are congruent
so are the corresponding chords
The tangent-secant theorem
given an angle with its vertex on a circle, formed by a secant ray and a tangent ra, the measure of the angle is half the measure fo the intercepted arc.
the two-tangent
if two tangent segments to a circle from a point of the exterior are congruent and determine congruent angles with the segment from the exterior point to the circle
the median concurrence theorem
medians of triangles when intercepted is two thirds the way
if two arcs have equal radii
then their lengths are proportional to their measuers