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95 Cards in this Set
 Front
 Back
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

0180


Angle Addition Postulate

Selfexplanatory


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


306090

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

454590 is 11square 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 linecircle 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 tangentsecant 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 twotangent

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
